Place a rack in the center of your oven and preheat to 350°F. Coat an 8x8-inch baking dish with nonstick spray, then line with parchment so that two opposite sides of the parchment overhangs the pan like handles.
In a medium saucepan, combine the cranberries, maple syrup, lemon juice, and salt. Bring to a simmer over medium-low heat, stirring regularly and gently pressing on the cranberries to break them down.
When the mixture is saucy and the berries are mostly broken down, about 6 minutes, stir in the cornstarch. Return to a simmer, stirring constantly, until the mixture is thickened, 1 to 2 minutes. Transfer to a bowl to cool.
For the crust and topping, in a mixing bowl, combine the flour, oats, sugar, baking powder, and salt until well combined. Add the melted butter and mix (I like to use my hands) until the mixture sticks together when pressed and you have some larger chunks (about the size of a quarter) and smaller bits (closer to pea-sized).
Transfer two-thirds of the dough mixture to the prepared baking dish and press into an even layer in the bottom of the dish. Cover with the cranberry filling. Sprinkle the remaining crumble over the filling.
Bake for 20 to 25 minutes, until golden on top and firm in the center—there should be very little movement in the center when you jiggle the pan. Cool in the pan for 30 minutes, then use the parchment handles to carefully transfer to a wire rack. Let cool to room temperature before slicing into squares and serving.
Notes
TO STORE: Transfer the bars to an airtight container and store at room temperature for 3 to 4 days. You can place parchment between the layers if you need to stack them.
TO FREEZE: For best results, wrap the bars individually in plastic wrap and place them in an airtight container or freezer bag. Freeze for up to 6 months and thaw at room temperature to enjoy.
TO MAKE AHEAD: You can make the filling up to 5 days in advance and store it in an airtight container in the refrigerator.