Preheat the oven to 350 F. Grease an 8" square cake pan, set aside.
Combine the first four ingredients in a small bowl. Set aside.
Zest and juice the lemon. Combine its zest and juice with the eggs, coconut milk, 2 tbsp coconut oil, and vanilla extract. Whisk until thoroughly combined.
Gently stir the dry ingredients into the wet ingredients. Reserve 1/3 cup of the batter, press the rest into the bottom of the greased cake pan. Blind bake in the preheated oven for thirty minutes, until browned and firm.
Remove from the oven, and top with the blackberries. Spoon the remaining batter over and around the blackberries. Return to the oven, and cook for an additional 30 minutes, until browned.