Preheat the oven to 350°F (175°C) and line an 8x8-inch baking dish with parchment paper.

In a large mixing bowl, combine flour, oats, brown sugar, granulated sugar, baking powder, and salt. Add butter and vanilla; mix until crumbly.

Press half of the crumb mixture into the bottom of the prepared baking dish. Bake for 20 minutes until lightly golden.

In a medium saucepan, combine blueberries, granulated sugar, cornstarch, and lemon juice. Cook over medium heat until thickened, about 5-7 minutes.

Spread the blueberry filling over the warm crust and sprinkle remaining crumb mixture on top.

Bake for an additional 30-35 minutes until topping is golden brown and filling is bubbly.

Cool completely at room temperature for at least 1 hour before slicing into squares.