Set an 8-inch cake ring (with 2-inch sides) on a rimmed baking sheet lined with parchment paper.
On a lightly floured work surface, roll out dough to 1/4 inch thick. Cut out a 12- inch circle. Fit circle into cake ring, pressing dough onto baking sheet and up sides of ring; trim dough flush with top edge of ring. Prick bottom all over with a fork. Freeze until firm, about 30 minutes. Preheat oven to 400 degrees.
Line tart shell with parchment paper, and fill with pie weights or dried beans. Bake until dough starts to feel firm on edges, about 20 minutes. Remove parchment and weights; continue baking until crust is pale golden brown, about 15 minutes. Let cool completely on a wire rack. Leave oven on.
Whisk ricotta, milk, eggs, zest, salt, and pepper in a large bowl. Stir in arugula. Pour mixture into tart shell; bake until puffed and pale golden brown, about 45 minutes. Let cool at least 30 minutes before serving. Serve with arugula salad.