Preheat the oven to 350 F and prepare an 8 x 8 baking dish by lightly greasing or lining with parchment paper.
Stir together the flour, sugar, baking powder, and salt. Cut in the butter with a pastry blender or fork until evenly incorporated and the butter is in crumbs roughly the size of peas.
Beat the egg separately, then stir into the flour mixture with a fork.
Press about 1/2 to 3/4 of the mixture into the bottom of the baking dish.
Cut the blackberries in half, then toss them in the lemon juice. Add the sugar and toss again to coat. Sprinkle them over the crust in the pan.
Sprinkle the remaining dough mixture over the blackberries.
Bake until it just about passes the toothpick test (a few moist crumbs are good to have around), about 40 minutes. Let cool completely in pan before cutting.
The bars can keep at room temperature in an airtight container for about 3 days. You can refrigerate them to keep them longer, but it'll change the texture.
