Preheat oven to 400°. (If pastry is in 2 sheets, cut 1 sheet in thirds along fold lines. On a lightly floured board, overlap pieces slightly with second sheet--1 piece at a short side and 2 pieces end to end along a long side. Trim to fit, then press to join.) Roll pastry on floured board into a 12- by 16-in. rectangle. Lift pastry to a large baking sheet lined with parchment paper.
Cover pastry with another piece of parchment and a metal cooling rack turned upside down. Bake until pastry is golden all over, about 15 minutes.
Remove cooling rack and top sheet of parchment. Arrange prosciutto on pastry to cover. Bake until pastry is golden brown with no raw-looking spots in center, about 15 minutes; prosciutto will shrink. Gently press down any large air bubbles. Slide pastry on parchment to a rack and cool at least 10 minutes.
Combine ricotta, pepper, lemon zest, and 1/4 tsp. salt in a bowl. Dollop small spoonfuls of ricotta evenly over pastry, leaving border clear, then smear ricotta a bit (it shouldn't cover completely).
Arrange tomatoes over ricotta. Sprinkle with remaining 1/4 tsp. salt. Drizzle with oil and sprinkle with chives and basil. Cut into pieces.
Make ahead: Through step 3, up to 2 hours.