Spray a 9x13 pan with non stick spray. Line the bottom and up the side with parchment paper if desired to help pull the bars out later. (Just paper up two sides is fine to lift them out).
Mix all of the berries in a medium bowl with 1/2 cup sugar, juice from 1/2 lemon (approximately 1 Tablespoon), and 1 Tablespoon flour. Set aside.
In a large bowl, combine 3 cups of flour, 1/2 cup sugar, 1/2 cup brown sugar, 1 teaspoon baking powder, 1 teaspoon cinnamon, and 1/4 teaspoon salt. Stir to combine.
Whisk the egg and vanilla together in a small bowl and add to the flour mixture. Stir to combine.
Cut the cold butter into Tablespoon pieces (or smaller) and add to the flour mixture. Use a pastry cutter or fork to work the butter into the four. Use your hands if desired. Continue until the butter is in very small pieces and the flour resembles coarse sand.
Pour between 1/2 to 2/3 of the flour mixture into the baking dish. Press the mixture into the bottom of the pan to form an even layer.
Add the berries into the dish and spread out across the crust.
Take the remaining dough mixture and squeeze in your hand to create clumps, then crumble the clumps (to make small clumps) across the top of the berry mixture until most is covered.
Bake the crumble bars for approximately 35-40 minutes until the top is browned and the edges of the berry mixture are bubbling.
Let cool completely or until just slightly warm. Re-warm if desired in pieces or as a whole. Serve with ice cream or whipped cream if desired.