Preheat the oven to 350°F (175°C). Grease and flour a 9-inch square or 9-inch round cake pan. Alternatively, line the pan with parchment paper, leaving an overhang to easily lift the cake out later.
Place the butter in a large, microwave-safe bowl. Microwave in 30-second intervals until it is about 90% melted but not completely liquid.
Add the 1 cup of granulated sugar to the butter and whisk vigorously for a full 30 seconds.
Add the salt and vanilla extract, and whisk for another 30 seconds.
Add the room-temperature eggs one at a time, whisking well to fully incorporate each egg before adding the next. After the last egg is in, whisk for a full minute until the batter is light, creamy, and you can see air bubbles.
Sift the cake flour, powdered sugar, and baking powder directly into the wet ingredients. Add the sour cream.
Fold the batter with a rubber spatula until it is smooth and just combined. Be careful not to overmix.
Pour the batter into the prepared pan and smooth the top. Sprinkle evenly with the additional 3 tablespoons of granulated sugar.
Bake for 30-45 minutes, or until the top is golden brown and a cake tester or wooden pick inserted into the center comes out with moist crumbs attached or clean.
Let the cake cool in the pan on a wire rack for 15 minutes before inverting it onto the rack to cool completely