While the cake is baking place the butter in a medium saucepan over medium-low heat. When the butter is melted and begins to boil begins swirling (or stirring) the pan to prevent the fat solids from sticking to the bottom of the pan and burning. Continue cooking the butter until it becomes a deep amber color. Remove from the heat and cool for 5 minutes. Place the pan in the refrigerator so the butter chills and becomes solid again.
When you’re ready to make your frosting remove the butter from the fridge and allow the butter to sit at room temperature for 10 minutes to take the chill off.
Scrape the browned butter into the bowl of your stand mixer fitted with the paddle attachment. Mix on medium speed until creamy. Turn the mixer to low and add in the powdered sugar.
Slowly add in the maple syrup and turn the mixer up to medium to mix until creamy, scraping the sides of the bowl as necessary.
Assembly
Level one of the cakes with a serrated knife. Place this layer on a cake plate. Top this layer with a little less than half of the frosting and smooth with an off-set spatula. Place the remaining cake on top and top that with the rest of the frosting.
Drizzle a little more maple syrup on top if desired.
