In a food processor, pulse together 1 1/2 cups flour, powdered sugar, and salt. Add 8 tablespoons butter and pulse until it resembles cornmeal.
Pulse in egg until a soft, crumbly dough forms. Dump dough into prepared pan and press evenly to cover bottom. Prick all over with a fork, chill in the freezer for 10 minutes, then bake at 375°F for 10 minutes. Let cool slightly.
Meanwhile, combine raspberries and 2 tablespoons brown sugar in a medium bowl. Stir gently, smooshing some of the berries, and let rest while crust bakes and cools.
Once crust has cooled, spoon raspberries with their juices over the top.
In a food processor, pulse together 1/3 cup flour, 2 tablespoons brown sugar, granulated sugar, and 2 tablespoons butter until coarse crumbs are formed. Scatter crumb over the top of the raspberries.
Bake at 375°F for 30 minutes, until golden brown. Let cool completely before cutting.
Notes
If using frozen raspberries in place of fresh, be sure to thaw completely and drain excess water before using.