Preheat the oven to 350℉ and line a 9x9-inch metal cake pan with parchment paper, making sure it rises above the sides for easy lifting after baking, and set aside.
In a stand mixer fitted with a paddle attachment, cream together 11 tablespoons unsalted butter, 1⅔ cups granulated sugar, 1 tablespoon vanilla bean paste, and ½ teaspoon salt on medium-high speed for about 2 minutes. A large mixing bowl with an electric mixer may also be used.
Add the 2 large eggs one at a time, mixing at high speed for 45 seconds after each addition, then mixing at high speed for 3 minutes. Scrape down the sides and bottom of the bowl.
In a medium bowl, whisk together 2 cups all-purpose flour and ¾ teaspoon baking powder. Add a third of the flour mixture to the mixing bowl and mix, followed by half the ¾ cup sour cream, mix again, and repeat the additions, ending with the last third of the flour. Use a rubber spatula to scrape down the sides and bottom of the bowl, fold the batter, and make sure everything is evenly mixed.
Transfer the batter to the prepared baking pan and sprinkle with a generous coating of granulated sugar.
Bake for 40 to 50 minutes or until the center of the cake reaches 200℉ and the top is crunchy and golden brown. Allow the cake to cool in the pan for 15 minutes before lifting out with the parchment and cooling completely on a wire rack.
Slice and serve with fresh berries and whipped cream.