Williams-Sonoma's Brown Butter Cake

I used this recipe to make my snowman cake this year. Added May 23: I've finally made this without using my snowman cake pan, and have added the instructions below the original recipe.

• Ready In: 3 hrs
• Serves: 12-14

Ingredients

• 32  tablespoons unsalted butter
• 3  cups all-purpose flour
• 2  teaspoons baking powder
• 1 1⁄4 teaspoons salt
• 1 1⁄4 cups milk
• 1  tablespoon vanilla extract
• 1 2⁄3 cups granulated sugar
• 3⁄4 cup  firmly packed light brown sugar
• 4  eggs

Directions

1. Have all the ingredients at room temperature.
2. In a saucepan over medium heat, melt the butter, then cook until the solids separate and settle on the pan bottom, 3 to 5 minutes.
3. Continue to cook until the solids brown and are almost burnt, 18 to 20 minutes more.
4. Pour the brown butter into a bowl, leaving the solids in the pan (discard the solids).
5. Let the butter cool at room temperature until firm.
6. The brown butter can be prepared up to 2 days in advance; cover and refrigerate until ready to use.
7. Bring to room temperature before using.
8. Position a rack in the lower third of an oven and preheat to 325°F
9. Brush the pan with unsalted vegetable shortening and lightly flour.
10. Tap out excess flour.
11. Over a sheet of waxed paper, sift together the flour, baking powder and salt.
12. In a small bowl, combine the milk and vanilla.
13. Set aside.
14. In the bowl of an electric mixer fitted with the flat beater, beat the brown butter on medium speed until creamy and smooth, 1 to 2 minutes.
15. Add the granulated sugar and brown sugar and continue beating until light and fluffy, about 5 minutes, stopping the mixer occasionally to scrape down the sides of the bowl.
16. Add the eggs one at a time, beating well after each addition.
17. Reduce the speed to low and add the flour mixture in three additions, alternating with the milk mixture and beginning and ending with the flour.
18. Beat each addition just until incorporated, stopping the mixer occasionally to scrape down the sides of the bowl.
19. Spoon the batter into the prepared pan, dividing it evenly between the two halves. Bake until the center of the cake springs back when touched and a toothpick inserted into the center comes out clean, 55 to 60 minutes.
20. Transfer the pan to a wire rack and let the cake cool in the pan for 15 minutes.
21. Tap the pan gently on a work surface to loosen the cake.
22. Set the rack over the top of the cake, invert the pan onto the rack and lift off the pan.
23. Let the cake cool completely, 3 to 4 hours, before assembling and decorating with vanilla buttercream.
24. If you're using a 9x13 pan:
25. Butter and flour pan.
26. Spoon cake mix into pan and smooth out.
27. Bake at 325°F for 30-45 minutes, using a toothpick to test doneness.
28. Cool for 15 minutes and remove from pan; setting cake on cooling rack to cool completely.
29. Frost as desired.