Preheat the oven to 375°F, 190°C, or gas mark 5. Line the inside of the 8 x 8 inch baking pan with parchment paper and set aside.
In a medium bowl, combine the sugar, flour, almond flour, baking powder and salt.
Add the flour mixture to a food processor, add the butter and blend until the butter is the size of pebbles. Work with the dough until the pieces are very small. The dough will be crumbly.
Beat the eggs and vanilla together and pour over the dough mixture. Mix until combined. The dough will still be crumbly and will not create an even mixture.
Place ⅔ of the mixture in the baking dish and pat down.
In a mixing bowl place the blackberries, lemon zest, cinnamon, cornstarch, and brown sugar and gently toss to coat the blackberries and pour over the bottom crust.
Crumble the remaining dough over the blackberry filling layer.
Bake until top is golden brown, about 40- 45 minutes.
Allow to cool completely before removing from the baking dish and slicing.