Preheat oven to 350°F (175°C). Line an 8x8-inch pan with parchment paper, leaving overhang.
Make the crumble base: In a large bowl, whisk together flour, oats, brown sugar, granulated sugar, baking powder, and salt.
Add wet ingredients: Pour in melted butter and vanilla. Mix with a fork until crumbly, with some larger clumps.
Form crust: Press 2/3 of the crumble mixture into the prepared pan to create a firm, even base.
Prepare filling: In a medium bowl, gently combine raspberries, cornstarch, lemon juice, and 1 tbsp granulated sugar. Stir carefully to avoid crushing berries.
Assemble: Spread raspberry filling evenly over the crust. Sprinkle remaining crumble over the top, leaving some berries visible.
Bake: Bake for 30–35 minutes, until the top is golden and the filling is bubbling at the edges.
Cool completely: Let bars cool in the pan for at least 2 hours before slicing.