Preheat oven to 350 degrees F (175 degrees C). Grease two 8-inch round cake pans and line with parchment paper.
Beat 3/4 cup butter and white sugar together in a large bowl with an electric mixer until pale and creamy, about 2 minutes. Add eggs one a time, mixing well between each addition. Add 1 teaspoon vanilla extract; beat briefly until well-blended in the batter. Continue beating batter until bubbles appear on the surface, about 2 minutes more.
Sift flour, baking powder, and salt into the bowl. Gently fold with a spoon just until smooth. Divide the batter evenly between the prepared pans, smoothing the tops with a cake spatula.
Bake in the preheated oven until cakes are golden brown and a toothpick inserted into the center comes out clean, about 20 minutes. Cool in the pans for 5 minutes before inverting onto a wire rack to cool completely, about 30 minutes.
Beat confectioners' sugar, 1/4 cup butter, and 1 teaspoon vanilla extract together in a bowl to make a smooth buttercream.
Place one cake layer, flat-side up, on a serving platter. Spread buttercream evenly onto the cake with a spatula. Spread raspberry jam in an even layer over the buttercream, right to the edges. Place second layer, flat-side down, over the filling.