Italian Rice Pie (Pastiera di Riso)

Pulse flour, sugar, baking powder, and salt in a food processor until combined. Add butter and pulse until mixture resembles coarse meal with some roughly pea-size butter lumps. Add eggs and pulse until just incorporated and dough begins to form large clumps. Turn out dough onto a work surface and divide into 6 portions. With heel of your hand, smear each portion once or twice in a forward motion to help distribute fat. Gather dough together, using a pastry scraper if you have one, and form into a thick log. Cut off 2/3 of the log and form into a large rectangle for the bottom of the pie. Form the remaining piece into a smaller rectangle for the top of the pie. Chill each, wrapped in plastic wrap, until firm, at least 30 minutes.