Preheat the oven to 350, and spray the bottoms of three 8-inch cake pans with non-stick spray.
In a saucepan over medium heat, melt the butter. Continue to cook the butter, swirling the pan occasionally, for about 10 minutes, until the water has evaporated, and the butter is forming nutty, fragrant golden brown solids at the bottom of the pan. Remove the pan from the heat and let the butter cool for 10 minutes.
In a large bowl, whisk together the pumpkin, brown sugar, granulated sugar, eggs, buttermilk and vanilla. Whisk in the browned butter.
In a separate bowl, sift together the flour, baking soda, salt and spices.
Add the dry ingredients to the wet, and whisk for about 30 seconds until smooth.
Divide the batter between the pans. Bake the cakes on the center oven rack for about 22 minutes, until a cake tester or toothpick comes out clean.
Set the pans on a wire cooling rack, cover loosely with a clean kitchen towel, and cool completely before frosting.