Preheat oven to 350°F (175°C). Grease a 9x9-inch (or 8x11-inch) square baking pan and line with parchment, leaving an overhang for easy removal. Lightly grease the parchment.

Combine dry ingredients

In a large bowl, whisk together the all-purpose flour, 3/4 cup granulated sugar, baking powder, baking soda, and salt until evenly distributed.

Mix wet ingredients

In a separate bowl, whisk the eggs until combined. Add the milk, Greek yogurt (or sour cream), melted butter, and vanilla extract; whisk until smooth and homogeneous.

Combine wet and dry

Pour the wet mixture into the dry ingredients and fold gently with a spatula until just combined. Do not overmix — a few small lumps are fine. The batter will be thick but pourable. If it seems too thick, add up to 2 tablespoons additional milk.

Spread in pan

Spoon about two-thirds of the batter into the prepared pan and spread evenly with an offset spatula to form a smooth base layer. Reserve the remaining batter for the top layer.

Fruit Filling

Prepare fruit mixture

In a medium bowl, gently toss the berries with 1/4 cup granulated sugar, cornstarch, lemon juice, and lemon zest until the berries are coated and the cornstarch is evenly distributed. Let sit 5 minutes to macerate and thicken slightly.

Layer fruit

Evenly spread the berry filling over the base batter in the pan. Try to leave a small border (about 1/4 inch) from the edges so the top batter can adhere.

Finish & Bake

Top with remaining batter

Drop the reserved batter by spoonfuls over the berry layer. Use an offset spatula to gently spread it to cover most of the fruit — it’s okay if some fruit peeks through. The top layer will be slightly thinner than the base.

Brush and sugar top

Lightly brush the top with 1 tablespoon melted butter and sprinkle 2 tablespoons turbinado or coarse sugar evenly over the surface to create a crisp, golden finish.

Bake

Bake in the preheated 350°F (175°C) oven on the middle rack for 35–45 minutes, or until the top is golden brown and a toothpick inserted into the cake (avoiding large pockets of fruit) comes out with a few moist crumbs but no raw batter. If edges brown too quickly, tent loosely with foil for the last 10 minutes.

Cool and finish

Remove from oven and set on a wire rack. Let cool in pan for 20–30 minutes, then use the parchment overhang to lift the cake from the pan and cool further on the rack for another 20 minutes. Dust with powdered sugar if desired, slice into 9 squares and serve warm or at room temperature.