Step 1Place a large cast-iron skillet in the middle of the oven and heat it to 500 degrees. This will take about 30 minutes.
Step 2In the meantime, prepare the mushrooms. With a damp towel wipe off any dirt. If you must rinse them, do so gently and pat dry.
Step 3Create various shapes: Slice crimini and button mushrooms in half. Remove the bottom tuft of the king oyster mushrooms and discard, then slice lengthwise into four or five long pieces before cutting down the middle so you have short rectangles. Rip the oyster mushrooms into halves by hand. Slice the portobello into quarters or eighths as desired.
Step 4Remove the pan and add all the mushrooms. Return it to the oven for five minutes. Then remove again, and stir the mushrooms so that any sides unexposed to the hot iron get a good sear. Cook for an additional five minutes.
Step 5Remove the pan and add the shallots and butter, and toss. Return to the oven for another 5 minutes.
Step 6Final removal: Add the garlic and parsley, and set aside for 3 to 5 minutes to give the flavors time to marry. Salt generously and pepper profusely. This makes about 4 cups of mushrooms, more than you'll need for the remainder of the recipe.
Step 1In a large mixing bowl, combine the flour, water and yeast. The resulting goo should look wet and reckless. Wrap the bowl up and let it sit in the corner (preferably a warm one) just until the sponge becomes bubbly and thick, several hours or as long as overnight.
Step 1In a large bowl, whisk together the flour, salt, baking powder, baking soda, instant and brewer's yeast. Set aside.
Step 2In the bowl of a stand mixer fitted with the paddle attachment, or in a large bowl using a hand mixer, combine the sponge with the egg, water and melted one-fourth cup butter.
Step 3With the mixer running, slowly add the flour mixture until combined (you will need to switch to a dough hook if using a stand mixer, and may need to finish mixing by hand if you started with a hand mixer). The dough should be sticky and stretchy, but not very wet. If using a stand mixer, continue to mix until the dough is soft and smooth, adding flour a little at a time if necessary, about 5 minutes; if mixing by hand, turn the dough out onto a floured surface and knead until soft and smooth, about 7 minutes.
Step 4In yet another large bowl, add the teaspoon olive oil and give it a swirl. Form the dough into a ball, and roll it in the oil so that it's greasy everywhere. Cover the bowl with plastic and set it aside in a warm corner until puffed and roughly doubled in size, about 1 hour.
Step 5Meanwhile, prepare the mushroom filling: In a large saute pan, heat the remaining 2 tablespoons olive oil over medium-high heat until hot. Add 2 tablespoons butter and swirl the pan until the butter melts. Add the shallots and cook, stirring frequently, until the shallots are caramelized, 12 to 14 minutes. Off heat, stir in the cream sherry, then cook until the sherry is reduced by half. Stir in the cast-iron mushrooms, then remove from heat and set aside to cool.
Step 6Form the rolls: On a floured surface, gently roll out the dough into a 12-by-18-inch rectangle. Spread the sherry-butter-shallot-mushroom goo all over the giant dough rectangle. Make sure to spread evenly all the way to the edges. Apply the dill and the cheese in a similar fashion; evenly distribute all the way to the corners of your dough sheet.
Step 7Sprinkle salt and grind pepper all over the thing and heat the oven to 350 degrees.
Step 8Carefully roll the rectangle lengthwise into itself. Start at the long bottom and curl inward until you have a bulging log. Use a sharp knife and slice rolls off of the left side of the log. You can make them as thick as you'd like; we like ours about 2 inches thick.
Step 9Gingerly place the rolls side by side (don't crowd -- they should barely touch each other to give them room to expand) on a greased (with butter) baking pan, and cover them loosely with plastic.
Step 10Set the rolls aside until they have puffed, at least 30 minutes, then slide the rolls into the oven. Bake until the rolls are richly golden and smell amazing, 30 to 50 minutes, depending on the thickness of the rolls and how they are arranged in the baking pan. To test for doneness, stick a knife in a center roll or two -- the filling will be somewhat oozy, but the dough should be baked.