Preheat the oven to 350°F (175°C). In a large mixing bowl, combine gluten-free flour, rolled oats, brown sugar, salt, and baking powder. Mix well. Pour in melted butter and vanilla extract, stirring until it resembles coarse crumbs. Reserve 1 cup of this mixture for topping. Press the remaining mixture into the bottom of a prepared baking dish.
In a separate bowl, combine raspberries, lemon juice, cornstarch, and granulated sugar. Gently toss to coat the raspberries. Spread the raspberry filling evenly over the crust in the baking dish. Sprinkle the reserved crumb mixture over the raspberry layer.
Bake for 30-35 minutes, or until the top is golden brown and the raspberries are bubbly. Allow to cool completely in the pan before cutting into squares.