How to Make It
Stir together flour, salt, and sugar in a medium bowl. Using a pastry cutter, cut in chilled cubed butter until butter resembles small peas. Using a fork, stir in 1/4 cup ice water. Stir in up to 1/4 cup more ice water, 1 tablespoon at a time, just until dough comes together. Shape dough into a disk, and wrap tightly in plastic wrap. Chill at least 2 hours or up to 3 days.
Preheat oven to 400°F. Toss together mushrooms, olive oil, herb sprigs, 1 1/4 teaspoons salt, and 1/4 teaspoon pepper on a rimmed baking sheet; spread into an even layer. Bake in preheated oven until mushrooms are just tender, about 20 minutes. Discard herb sprigs; set mushrooms aside to cool to room temperature, about 15 minutes.
Reduce oven temperature to 325°F. Unwrap dough, and turn dough out onto a lightly floured surface. Roll into a 15-inch circle, about 1/4 inch thick. Stir together drained ricotta, remaining 1/2 teaspoon salt, and remaining 1/4 teaspoon pepper. Spread ricotta mixture on dough, leaving a 2-inch border. Layer roasted mushrooms over ricotta; sprinkle with chopped thyme, rosemary, and sage. Fold edges of dough up over filling, pleating every 2 inches. Lightly brush edges of dough with beaten egg.
Bake at 325°F until crust is golden brown, 50 minutes to 1 hour. Remove from oven, and transfer to a wire rack to cool 10 minutes. Serve warm or at room temperature.