Preheat oven to 350 degrees F. Lightly grease a light-colored metal 9X13-inch baking pan with cooking spray (can line with parchment and grease parchment, if desired). If using a glass pan, preheat oven to 325 degrees F.
In a large bowl, add the melted butter, 1 3/4 cups granulated sugar, sour cream, eggs, lemon zest, and vanilla. Whisk together until well-combined.
Add the flour, baking powder, salt, and baking soda. Stir with a spatula until the dry ingredients are mostly combined but a few dry streaks still remain (don't over mix in this step).
Add the fresh berries. Gently fold and mix until the berries are evenly combined and no dry streaks remain. It's ok if the berries break apart a little bit, but try to mix slowly and carefully to keep the berries from disintegrating into the batter.
Spread the batter evenly in the prepared pan.
Sprinkle the remaining 1/4 (to 1/3) cup granulated sugar evenly over the top of the batter.
Bake for 40 to 45 minutes until the cake is lightly golden and puffed and a toothpick inserted in the center comes out clean or with moist crumbs. Add additional time, if needed (may need extra time for a glass pan).
Let the cake cool in the pan. Serve squares of cake at room temperature with fresh berries, whipped cream, or vanilla ice cream, if desired.
Notes
Butter/Oil:The melted butter can be replaced with a neutral-flavored oil. If doing so, increase the salt in the recipe to 3/4 teaspoon.Lemon Zest:This ingredient adds a delightful hint of fresh citrus that compliments the berries so well. You can leave it out if you don't have it, but I encourage you to use it if you can.Berries:Fresh berries work best in this cake since they are more firm than frozen berries and don't give off as much liquid. However, you can experiment with frozen berries. I would recommend adding them frozen, but you could also try thawing and patting dry before using. You can experiment with other types of berries, like blackberries or strawberries. Other fruits like peaches and nectarines might work well in this cake also.