1 ½ cups all-purpose flour (about 6 3/8 ounces), plus more for work surface

½ cup unsalted butter (4 ounces), chilled and cut into 1/2-inch pieces

1 ¼ ounces Parmigiano-Reggiano cheese, finely grated on box grater (about 1/2 cup)

1 ½ pounds firm-ripe red Anjou pears (unpeeled), cored and cut into 3/4-inch-thick wedges (see Note)

1 teaspoon grated lemon zest plus 1 tablespoons fresh lemon juice (from 1 lemon)

Whisk together flour and salt in a large bowl. Using your fingers, rub butter into flour mixture until butter forms pea-size pieces. Add cheese, and toss to incorporate. Stir together 3 tablespoons ice water and vinegar in a small bowl, and add to flour mixture. Using your hands, gently mix flour mixture until a shaggy dough forms. Gently knead dough by pressing the heel of your hand into the dough so it compacts against the base of the bowl and comes together. Transfer dough to a lightly floured work surface, and shape into a 6-inch disk (about 1/2 inch thick). Wrap tightly in plastic wrap. Chill at least 1 hour or up to 5 days.

Preheat oven to 400°F with rack in lower third position. Unwrap dough, and transfer to a lightly floured work surface. Roll into a 14-inch round, flouring dough as needed to prevent sticking. Transfer to a parchment paper–lined rimmed baking sheet. Place dough in refrigerator until ready to use.

Toss together pears, honey, butter, and lemon zest and juice in a large bowl. Sprinkle with cornstarch, pepper, and salt; stir until well combined.

Arrange pear filling in center of chilled pastry dough, leaving a 2-inch border. Fold uncovered dough edges inward by about 11/2 inches, pleating dough to form a crust and gently pressing to adhere. Brush crust lightly with beaten egg.

Bake in preheated oven until crust is golden brown and filling is thickened and bubbly, 30 to 35 minutes. Remove from oven; let cool at least 15 minutes or up to 12 hours. Drizzle with additional honey, and garnish with shaved cheese. Slice and serve.

Pastry dough can be made up to 5 days in advance and stored, wrapped tightly in plastic wrap, in refrigerator.

Firm-ripe pears will soften as they bake while also maintaining their shape.

Golden, candied orange peel–scented Passito di Pantelleria: Donnafugata Ben Ryé