Step 1 Dissolve the yeast in one-half cup of warm water. Sprinkle the sugar over the mixture and stir. Allow to stand until bubbly, 10 to 15 minutes, then stir in 1 tablespoon of the olive oil.
Step 2 In a large mixing bowl or in the bowl of a stand mixer, combine the flour, 3 teaspoons thyme and 1 teaspoon salt. Add the yeast mixture to the flour along with an additional one-half cup warm water and mix to combine.
Step 3Turn out the dough onto a board and knead by hand, or continue to mix using a dough hook, until smooth and satiny, about 5 minutes. Place the dough into an oiled bowl and cover loosely with plastic wrap, then allow to rise until doubled, about 45 minutes.
Step 4While the dough is rising, prepare the mushroom filling. Heat 2 tablespoons of the oil in a large, heavy sauce pot over medium-high heat until hot. Add the mushrooms and three-eighths teaspoon salt. Saute, stirring, until the mushrooms are lightly browned and dry, about 5 to 8 minutes. Remove from the heat and set aside.
Step 5To the pot, add the remaining tablespoon oil along with the pancetta and saute over medium heat until caramelized and crispy, 5 to 6 minutes. Add the shallots and garlic and saute until they are tender and fragrant, 1 minute. Stir in the reserved mushrooms and the remaining half-teaspoon of thyme. Season to taste with salt and freshly ground black pepper, then cool to room temperature.
Step 6Heat the oven to 400 degrees. Punch down the dough and divide it in half. Roll out each half to one-eighth-inch thickness, then cut out rounds using a 2 1/2 -inch cutter. You should have 2 1/2 dozen rounds from each half.
Step 7Assemble the calzones: Lightly brush the edges of half of the rounds with the beaten egg, then top with a generous teaspoon of mushroom filling and a half-teaspoon of cheese. Top each mound with another round of dough, pressing the edges together to seal completely. Brush each calzone with the beaten egg, then top with a sprinkle of fresh ground pepper. Make a small slit in the center of each calzone to form a vent and place them on a parchment-lined baking sheet. Bake 15 to 20 minutes or until lightly browned. Serve warm.