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In a large bowl, toss together the baking powder, graham cracker crumbs, ⅔ cups flour, and ⅓ cup brown sugar. Using your fingers, rub the ½ cup of butter through the dry ingredients. Spread the blueberry compote on top of the shortbread layer. Press the crumble mixture together in handfuls, so it holds together and break off chunks of crumble all over the top of the prepared blueberry compote filling. Press down lightly and bake for 20-25 minutes at 350 degrees or until the top is golden brown. Cool completely in the pan before cutting into squares or bars.