Heat oven to 350°F. Grease a 9-inch square pan and line the bottom with parchment.
Make the crumb: Stir flour, both sugars, cinnamon, and salt. Cut in cold butter until clumpy; chill.
Whisk batter dry ingredients: flour, cornmeal, sugar, baking powder, baking soda, salt, and lemon zest.
In another bowl, whisk eggs, sour cream, buttermilk, vanilla, and melted butter until smooth.
Fold wet into dry just until no dry spots remain; avoid overmixing.
Toss berries with 1 tbsp flour, then gently fold into the batter.
Spread batter in pan and crumble the topping evenly over the surface.
Bake 40 minutes, rotating once, until golden and a tester comes out with a few moist crumbs.
Cool in pan 20 minutes. Lift out, slice, and serve warm or at room temperature.