Place a baking sheet in the oven and heat to 400°F.
To make the crumble, whisk the flour, sugar, salt and baking powder in a medium bowl. Pour in the oil and use your fingers to combine, pinching the crumble together to form clumps. Freeze while you prepare the crust and berries.
To make the crust, whisk the dry ingredients in a large bowl. Whisk in the olive oil, water and vinegar.
Transfer the dough to a 9-inch pie plate and using your fingers, evenly press it over the bottom of the plate and up the sides.
To prepare the berries, whisk the sugar, cornstarch, and salt in a large bowl. Stir in the berries and lemon juice with a flexible spatula. Transfer the berries to the crust and crumble the topping over them. Place the pie on the preheated baking sheet and bake for 60 to 65 minutes, until the edges of the crust and the crumble are golden brown and the berries are bubbling between the crumbs in the center of the pie. If the crumb takes on too much color while the pie bakes, cover it in aluminum foil at the halfway point.
Bring the pie to room temperature before serving in order to ensure the filing is set. Serve slices with scoops of vanilla ice cream. The pie will keep tightly wrapped on the counter for up to 3 days.