Whisk 1 1/2 cups flour, 1 tablespoon granulated sugar, and 1/2 teaspoon salt in a large bowl. Cut in the cold cubed butter with a pastry blender until most pieces resemble peas, with a few flatter pieces remaining. Drizzle in 3 tablespoons ice water and toss with a fork. Add the remaining water 1 teaspoon at a time only until a squeezed handful holds together. Press the shaggy dough into a disk without kneading, wrap it, and refrigerate for 30 minutes.
On a lightly floured work surface, roll the chilled dough from the center outward into a 12-inch circle about 1/8 inch thick, rotating it frequently to prevent sticking. Transfer it to a 9-inch metal pie plate without stretching the dough. Ease it into the corners, trim the overhang to 1 inch, fold the edge under, and crimp firmly. Prick the base six times with a fork, then refrigerate the lined plate for 20 minutes while the oven heats.
Combine 3/4 cup flour, brown sugar, cinnamon, and 1/4 teaspoon salt in a medium bowl. Pour in the melted butter after it has cooled until warm rather than hot. Stir with a fork until no dry flour remains and uneven crumbs form, then squeeze several portions together to make larger clusters. Refrigerate the streusel while preparing the crust and filling. Chilling firms the butter, helping the crumbs remain distinct instead of melting into a continuous layer.
Position a rack in the lower third of the oven and heat it to 400°F. Set the chilled pie plate on a rimmed baking sheet, line the pastry with parchment, and fill it completely with pie weights. Bake for 18 minutes, then carefully lift out the parchment and weights. Bake 6 to 8 minutes more, until the base looks dry and matte but remains pale. Brush a thin, even layer of egg white over the hot interior and bake for 2 minutes, then reduce the oven to 375°F.
Whisk 3/4 cup granulated sugar, cornstarch, lemon zest, and 1/4 teaspoon salt in a large bowl until the cornstarch is evenly dispersed. Add the raspberries, lemon juice, and vanilla. Fold gently with a silicone spatula until the berries are evenly coated, taking care not to crush fresh fruit. Let fresh berries stand for 10 minutes so some juice moistens the starch. If using frozen raspberries, mix them only when the crust is ready and proceed immediately before they thaw.
Spoon the raspberry mixture and every bit of the collected starch mixture into the warm crust, spreading the berries into an even layer without pressing them down. Break the chilled streusel over the filling, distributing both small crumbs and larger clusters while leaving several narrow gaps where steam and bubbling filling can escape. Keep loose crumbs inside the pastry edge because pieces on the baking sheet can scorch. Return the assembled pie, still on its rimmed sheet, to the lower oven rack.
Bake at 375°F for 50 to 60 minutes. Rotate the baking sheet after 30 minutes for even browning, and loosely shield the pastry edge with foil if it becomes deeply golden before the filling is ready. The pie is done when the streusel is crisp and golden and the raspberry filling bubbles slowly through several gaps near the center for at least 5 minutes. Edge bubbling alone is not sufficient because the cornstarch in the center must become fully heated to thicken.
Transfer the pie plate from the baking sheet to a wire rack, keeping it level because the filling will be fluid while hot. Cool at room temperature for at least 4 hours, until the plate no longer feels warm and the filling has settled. Do not refrigerate the hot pie to speed this stage because trapped steam can soften the streusel and crust. Cut with a sharp knife, wiping the blade between slices, and lift each portion with a narrow pie server.
