Frosting: Melt the butter in a heavy-duty 1-quart sauce pan over medium heat. Cook swirling the pan occasionally until the butter turns a nutty golden brown; about 4 minutes. Pour into a small bowl and let stand until the solids settle at the bottom of the bowl; about 5 minutes. Carefully transfer to the freezer and chill until just firm; about 18 minutes. Using a spoon, carefully scrape the butter from the bowl, leaving the brown bits at the bottom. Using an electric mixer, beat the butter, cream cheese, brown sugar until light in color and the sugar has dissolved; about 2 minutes. Gradually beat in the confectioners' sugar and continue beating until fluffy; 1 to 2 minutes more.
To assemble the cake. Put one cake layer on a cake plate. Spread 1/2 C. frosting on the layer. Sprinkle 1/2 cup of the nut mixture over the frosting and top with the second layer. Frost top and sides of the cake with the remaining frosting. Arrange the remaining topping on the top of the cake.
Serve immediately or refrigerate for up to two days. Serve at room temperature.