Preheat the Oven: Preheat the oven to 180°C (350°F).
Prepare the Cake Batter: Add the very soft butter and granulated sugar to a mixer and blend together. Add the eggs, all-purpose flour, baking powder, vanilla extract, and milk, then blend until the ingredients are thoroughly combined and the batter is evenly mixed. Divide the Batter: Grease two 8-inch round cake pans and divide the batter evenly between them, spreading it out as evenly as possible.
Bake the Sponge Layers: Place the pans in the preheated oven and bake for 25–30 minutes, or until the sponge layers are baked through.
Cool the Cakes: Leave the cakes in their pans for 10 minutes, then carefully turn them out onto a cooling rack and allow them to cool completely.
Make the Buttercream: Combine the softened butter, ½ teaspoon vanilla extract, and ½ cup powdered sugar, then beat until the mixture is smooth and creamy.
Fill the First Sponge: Place one completely cooled sponge on a serving surface and spread the buttercream evenly over its top.
Add the Jam: Spread the ¼ cup raspberry or strawberry jam over the buttercream layer.
Assemble the Cake: Place the second sponge on top of the filling to create a sandwich, pressing it together gently.
Finish and Serve: Dust the assembled cake with a little powdered sugar immediately before serving.