In a small saucepan set over medium heat, brown the butter. Stir the butter occasionally until it turns amber in color and develops little brown specks.
Remove the butter from the heat and chill it in the freezer for 5 minutes.
Pumpkin Spice Cake
Preheat the oven to 350°F / 175°C. Butter and line an 8" square pan* with parchment paper.
Pour 113g of the brown butter into a medium sized mixing bowl, and set the remaining brown butter aside at room temperature.
Add in the sugar, oil, both eggs, the vanilla, pumpkin puree, and sour cream. Whisk until well combined.
Add in the flour, baking powder, salt, and pumpkin pie spice. Fold the dry ingredients into the wet, just until no flour streaks remain.
Pour the cake batter into the prepared cake pan. Bake for 25-30 minutes, or until a toothpick inserted in the center of the cake comes out clean.
Brown Butter Cream Cheese Frosting
In a small bowl, beat together the cream cheese, room temperature brown butter, and salt until the mixture is smooth.
Add in half of the powdered sugar and beat until combined, then beat in the rest of the powdered sugar, followed by the vanilla.
(Optional) Set aside a small amount of frosting to make little pumpkins on top. Dye some of the frosting orange, some green, and some brown. Transfer each color to a piping bag fitted with a small round tip.
Once the cake has fully cooled to room temperature, spread the brown butter cream cheese frosting over it. Decorate with mini pumpkins if desired, then serve, and enjoy!