Preheat the oven to 350°F and generously butter a 12-inch cast iron skillet, making sure to coat the bottom and sides well so the cake releases easily after baking.
To make the crumble topping, combine 1 cup all-purpose flour, ¾ cup packed brown sugar, and the zest of 1 lemon in a bowl. Cut in ½ cup softened butter until the mixture looks crumbly and resembles damp sand with small clumps. Set aside.
In a medium bowl, whisk together the dry cake ingredients: 2¼ cups all-purpose flour, 2 teaspoons baking powder, and ½ teaspoon salt.
In a large bowl, cream together ½ cup softened butter and 1 cup granulated sugar until light and fluffy. Add 1 egg, ½ cup sour cream, ¼ cup buttermilk, ¼ cup vegetable oil, 2 tablespoons lemon juice, 1 teaspoon vanilla extract, 1 teaspoon lemon extract (optional), and the zest of 2 large lemons, mixing until smooth and fully combined.
Gradually add the dry ingredients into the wet mixture, mixing just until combined. Do not overmix.
Gently fold in 1 cup frozen blueberries and 1 cup frozen raspberries, making sure they are evenly distributed throughout the batter. Do not thaw the berries before adding.
Pour the batter into the prepared cast iron skillet and spread it evenly. Sprinkle the crumble topping evenly over the batter, covering the surface completely.
Bake at 350°F for about 45 minutes, or until the top is golden brown and a toothpick inserted into the cake (avoiding berry pockets) comes out with a few moist crumbs.
Remove from the oven and allow the cake to cool in the skillet for at least 20 minutes before serving so it can fully set and slice cleanly.