How to Make It
In a large bowl, stir the wine, water, honey and yeast until the yeast is dissolved. Let stand until foamy, 5 minutes. Stir in the salt and the 1 tablespoon of olive oil. Add 1 cup of the flour and stir until a loose batter forms. Stir in the remaining 2 cups of flour until almost completely incorporated. Turn the dough out onto a work surface with any remaining flour and knead until the flour is incorporated and the dough is smooth and silky, 7 minutes. Transfer the dough to a lightly oiled large bowl and brush all over with olive oil. Cover with plastic wrap and let rise in a warm place until doubled in bulk, 1 hour and 30 minutes.
Scrape the dough out onto a lightly floured work surface and cut into 16 equal pieces. Roll the pieces into balls and transfer to a baking sheet. Cover loosely with plastic wrap and let stand for 15 minutes.
Working with 1 ball of dough at a time, roll it out on a lightly floured work surface to a 4-inch round, a scant 1/8 inch thick. Spoon 1 tablespoon of the ricotta on one half of the round, then top with 2 to 4 pepperoni slices and a heaping 1/2 teaspoon of the pesto. Fold the dough over to form a half moon and press the edge to seal tightly. Crimp the edge with a fork or pinch at intervals to make pleats. Transfer the calzone to a baking sheet and brush with the egg wash. Repeat with the remaining dough and filling to make the remaining calzones.
Preheat the oven to 325°. In a large saucepan, heat 1 1/2 inches of oil to 350°. Fry 4 calzones at a time, turning once, until browned and crisp, 3 to 4 minutes. Drain the calzones on paper towels and keep warm in the oven while you fry the rest. Serve hot.
The stuffed calzones can be prepared through Step 3 and frozen for up to 1 month. Let the calzones return to room temperature before frying.