In the bowl of a mixer, fitted with the paddle attachment, beat the butter and both sugars on medium speed until light and fluffy about 3 minutes. Add the eggs, one at a time, beating well after each addition, then add the vanilla and beat until incorporated. Scrape down the sides and bottom of the bowl and mix again for 30 seconds.
Divide the batter between the prepared pans and smooth the tops. Bake for 35 to 40 minutes, rotating the pans halfway, until toothpick inserted comes out clean. Transfer the pans to a wire rack and let cool for 20 minutes. Invert onto rack and let cool completely.
For the milk chocolate layers