For crust: In the work bowl of a food processor, pulse flour, sugar, and salt. Add cold butter; pulse until butter pieces are pea-size. Add egg and ¼ cup (60 grams) ice water; pulse until combined and a soft, but not sticky, dough forms.

Turn out dough onto a lightly floured surface, and knead until smooth. Shape one-third of dough (about 200 grams) into a disk; shape remaining dough into a disk, and wrap each disk in plastic wrap. Refrigerate for at least 1 hour or up to 2 days.

Lightly spray a 9-inch springform pan with baking spray with flour. Line bottom of pan with parchment paper.

For filling: In a large skillet, heat oil over medium-high heat. Add spinach; cook, stirring frequently, until wilted, about 2 minutes. Stir in garlic and pepper; cook, stirring occasionally, until fragrant and water has evaporated, 3 to 5 minutes. Remove from heat, and let cool completely.

In a large bowl, whisk together ricotta and eggs until smooth; stir in Parmesan and provolone.

On a lightly floured surface, roll larger portion of dough into a 14-inch circle (about ⅛ inch thick). Carefully transfer dough to prepared pan, pressing into bottom and up and over sides of pan to hold in place.

Layer one-third of ham in bottom of crust to cover. Top with ricotta mixture, spreading smooth. Top with spinach mixture and remaining ham.

In a small bowl, whisk together egg and 1 tablespoon (15 grams) water; brush onto top edge of dough.

On a lightly floured surface, roll remaining dough into an 11-inch circle (about ⅛ inch thick). Place on filling, gently pressing down to remove air. Firmly press dough layers together around edges to seal; trim excess dough to ½ inch beyond edge of pan. Roll edges of dough inward to crimp. Refrigerate until firm, at least 30 minutes.

Position oven rack in bottom third of oven. Preheat oven to 375°F (190°C).

Brush egg wash all over top of dough. Cut 3 (1½-inch) slits in top of dough.

Bake until golden brown and an instant-read thermometer inserted in center registers at least 155°F (68°C), 45 to 50 minutes. Let cool in pan on a wire rack for 15 to 20 minutes. Carefully remove sides of pan; serve warm, or let cool completely on a wire rack. Refrigerate in an airtight container for up to 3 days.