For Cake

1. Preheat the oven to 350°F. Line an 8 x 8” baking pan with parchment paper. Allow the sides of the parchment to extend over the edges of the pan by an inch or two for easy removal of the cake once baked. Set aside. 
2. In a large bowl whisk together the flour, granulated sugar, brown sugar, baking powder, baking soda, salt, cinnamon, ginger, nutmeg and cloves. 
3. Add the canola oil, pumpkin puree, eggs and vanilla to the dry ingredients. Whisk to combine but do not over mix. 
4. Transfer the batter to the prepared pan. Use an offset spatula to spread the batter into the corners of the pan and level the top. 
5. Bake in the center of the oven for 23 to 25 minutes. Check for doneness by inserting a toothpick into the center of the cake. It should come out clean or with a few crumbs remaining.
6. Remove the cake from the oven and set on a wire rack to cool completely before frosting.

For Frosting

1. To make the frosting, begin by browning the butter. Place the butter in a medium saucepan over medium-low heat. Stir every minute or so until the butter is melted. Continue stirring as the butter begins to foam and crackle, being careful not to walk away from the pan. The butter will turn a toasty, amber brown color and golden bits will begin to form in the bottom of the pan. Once the butter has reached this stage, remove the pan from the stovetop and scrape all of the butter and the brown bits into a large bowl. Do not let the butter get too brown, we want it to be golden brown and not too dark.
2. Place the browned butter in the refrigerator until firm but not solid. If the butter does return to a solid state, remove the bowl from the refrigerator and let it sit at room temperature for a few minutes before proceeding. 
3. Use a hand mixer on low speed to mix the brown butter until it resembles softened butter – creamy and smooth. There should be no hard chunks of butter in the bowl. 
4. Add the cream cheese and mix to combine. Add the vanilla and a pinch of salt and combine well. 
5. Add the powdered sugar one cup at a time, mixing on low speed to incorporate. Continue until all of the sugar has been added. The frosting will be thick. Once all of the sugar has been incorporated, add the milk one tablespoon at a time. Mix on medium high speed for one minute until light and fluffy. Add more milk until the desired consistency has been reached. The frosting should be thick but spreadable. 
6. Once the cake is completely cool, use an offset spatula or knife to spread/swirl the frosting evenly over the top of the cake. Sprinkle the top with cinnamon sugar or nutmeg if desired.