Preheat the oven to 350 F. Brush an 8-inch square baking dish with melted butter. In a bowl, whisk together flour, salt and baking powder. Set this aside.
In a large mixing bowl, beat together melted butter and 3/4 cup sugar using a hand whisk. Then beat in the egg, milk, and vanilla extract. Beat just until the ingredients are combined.
Add the flour mixture and using a spatula or a whisk, incorporate the ingredients gently. Fold in half of the berries to the batter gently, then pour it into the prepared baking dish.
Top the batter with the remaining berries, placing them in a single layer over the cake. Sprinkle the reserved sugar all over the top. Bake the berry cake at 350 F for 40 minutes, or until a toothpick tester comes out clean.
Serve the cake warm, topped with ice cream if desired. To store leftovers, cover the cake and place it in the fridge for up to 3 days.