Preheat the oven to 350 degrees. Grease two 8-inch round cake pans and line with parchment; grease the parchment. In a heavy, medium skillet, cook the butter over medium heat, swirling occasionally, until it smells nutty and turns golden-brown, 4 to 6 minutes. Pour the browned butter into a small bowl, leaving the sediment in the skillet. Let cool.
In a large bowl, mix together the pumpkin puree, raw sugar, brown sugar, buttermilk, eggs and 1/2 tsp. vanilla. In a medium bowl, mix together the cake flour, white whole wheat flour, pumpkin pie spice, baking soda and salt. Add the dry mixture to the pumpkin mixture and stir until just combined (do not overmix). Stir in the browned butter.
Divide the batter between the prepared cake pans and smooth the tops. Bake until the cakes pull away from the sides of the pans, about 25 minutes. Transfer to a rack to cool. Once the pans are cool to the touch, carefully invert the cakes onto the rack and let cool completely.
Meanwhile, using an electric mixer, whip the cream cheese and confectioners' sugar until fluffy, about 3 minutes. Add the cream and remaining 1/2 tsp. vanilla and whip until the frosting is thick and smooth, about 3 minutes.
Transfer 1 cake layer to a serving plate. Spread with half of the frosting, leaving a 2-inch border around the edge of the cake. Gently top with the remaining cake layer. Spread with the remaining frosting, leaving a 2-inch border around the edge of the cake. Sprinkle with the hazelnuts.