Stuffing:
- 1/2 cup balsamic vinegar
- 1/2 cup soy sauce
- 2 cups sliced cremini mushroom caps
- 1 1/2 cups shredded Comté or Gruyère cheese, at room temperature
- Fresh thyme leaves
Bread:
- 3 1/2 cups white bread flour, plus extra as needed
- 1 1/2 teaspoons fine sea salt
- 1 1/2 teaspoons instant dry yeast
- 1 1/4 cups plus 2 tablespoons warm water (82° to 84°) plus up to 1/4 cup extra if needed
- Marinate the mushrooms: In a large, re-sealable bag, combine the balsamic vinegar, soy sauce and mushrooms. Seal the bag and shake to combine. Refrigerate 8 hours or overnight.
- Make the bread dough: In a large bowl, use your hand to combine the flour, salt and yeast. Make a well in the center of the dry ingredients and add the water. Use one hand to mix the dry ingredients into the water, using the other hand to rotate the bowl, stopping often to scrape down the sides of the bowl and your fingers as necessary until the dough comes together into a soft, sticky, wet mass. If the dough seems at all dry, add the remaining water 1 tablespoon at a time until the dough is quite loose and wet.
- Transfer the dough to your work surface. (Don't flour it first.) The dough will be very sticky; don't give in to the temptation to add more flour since that will alter the flour ratio of the dough. Hold you hands, palms facing up, at opposite sides of the dough mass that are closest to your body. Slide your fingers, still facing up, under the dough and lift the dough an inch or so from the work surface. Wrap your thumb around an index finger, creating a tight "OK" sign through the dough. While holding the "OK" sign, continue to curl your thumbs and index fingers tightly together to pinch off a portion of dough.
- Working as quickly and smoothly as you can, continue lifting and pinching the dough mass using the same technique, moving up the dough in approximately 5 to 7 times until you have gone through the entire dough mass. You should begin to feel the dough coming together. Turn the dough a quarter turn and continue lifting, pinching and turning the dough until it begins to take on an identifiable shape and is less and less sticky. This can take anywhere from 5 to 15 minutes.
- Using both hands, lift the dough up and fold it over onto itself in one swift motion, quickly dropping it down on the work surface. Repeat this process 4 to 5 times until a ball forms. Touch the dough with the back of your hand to make sure that it is no longer sticky; if it is sticky, use the "OK" sign pinching method to knead up and down the dough once or twice more, quickly folding the dough over itself 4 to 5 times.
- Lightly dust a large bowl with flour. Transfer the ball to the bowl, smooth side up, taking care to retain the round shape. Cover the bowl loosely with plastic wrap and set aside in a warm, draft-free place until the dough has doubled in volume, about 1 hour.
- Remove the marinated mushrooms from the refrigerator and drain them in a fine-mesh sieve.
- Lightly dust the work surface with flour. Transfer the dough to the floured work surface. If the dough is very sticky, flour your hands. Carefully and without ripping or tearing it, lift the dough and set it back down to see if it sticks. If it is, dust the work surface with more flour. Use the palm of your hand to press the dough into a 12-inch by 9-inch rectangle. Gently lift the dough to make sure it's not sticking; if it sticks, dust the underside with more flour. Divide the dough in half so you have two 6-inch by 9-inch rectangles. Lift the dough again to ensure it isn't sticking.
- Line 2 rimmed baking sheets with parchment paper. Turn the dough so the long side faces you. Layer half of the drained mushrooms down the center of the dough. Sprinkle half of the grated cheese over the mushrooms, then sprinkle with fresh thyme leaves. Using both hands, pick up each corner of the side of the dough closest to you. Very lightly pulling on the dough, fold it in, horizontally to the center of the rectangle, covering the mushroom-cheese stuffing. Using the heel of your hand, press down to firmly seal.
- Using your fingertips, pick up the far side of the dough and fold it halfway up and over the first fold, again with a very light pull on the dough. Using the heel of your hand, again press down firmly to seal. Gently pick up the dough and place it so the seam is on the side. Using the heel of your hand, firmly press the seam against the work surface to flatten and to create tension in the dough.
- Transfer the shaped dough to a prepared baking sheet, seam side down. Fill and shape the remaining piece of dough in the same way and place it on the other baking sheet, seam side down. Cover each baking sheet with a clean linen towel followed by plastic wrap.
- Set the baking sheets in a warm, draft-free place until your finger leaves a small indentation that slowly and evenly disappears, about 1 hour. Adjust an oven rack to the lowest position, place a baking stone on the rack and preheat the oven to 450°.
- Cut three 1-inch long lines on the surface of each loaf, just barely breaking through the skin and cutting about 1/8 inch into the surface of the dough. Place one sheet pan in the refrigerator. Slide the other loaf and the parchment paper onto the center of the stone, taking care not to touch the hot surface. Cover the loaf with a stainless steel mixing bowl and immediately close the oven door. Bake 10 minutes, then use a paring knife to carefully lift the edge of the bowl and use oven mitts to remove the bowl from the oven.
- Continue to bake until the bread is deep golden-brown with a crisp crust and sounds hollow when tapped on the bottom, 10 to 15 minutes more. An instant-read thermometer inserted into the center of the bread from the bottom should register between 185° and 210°. Transfer the loaf to a cooling rack and cool for at least 1 hour before slicing and serving. In the meantime, bake off the remaining loaf.