Prep the Oven & Pan: Preheat your oven to 350°F (175°C). Line an 8x8-inch baking pan with parchment paper, letting the sides extend over the edges for easy lifting later.
Mix Dry Ingredients: In a large bowl, whisk together the flour, granulated sugar, baking powder, baking soda, salt, cinnamon, ginger, nutmeg, and cloves. This creates your perfectly spiced dry base!
Combine Wet & Dry: Add the vegetable oil, pure pumpkin puree, eggs, and vanilla extract to your dry mix. Whisk gently until just combined – try not to overmix to keep the cake wonderfully tender.
Bake to Perfection: Pour the batter into your prepared pan and spread it evenly. Bake for 23-25 minutes, or until a toothpick inserted into the center comes out clean with just a few crumbs.
Cool Down: Let the cake cool completely on a wire rack. This is a crucial step before frosting to prevent any melty mishaps!
Brown the Butter (Frosting Magic!): In a small saucepan, melt the unsalted butter over medium-low heat. Stir frequently as it foams, crackles, and turns a beautiful golden-brown with nutty bits at the bottom. Immediately remove from heat and pour it into a heatproof bowl.
Chill the Butter: Place the browned butter in the fridge until it's firm but still soft enough to mix (not rock solid).
Whip the Frosting: In a mixing bowl, beat the chilled brown butter until creamy. Add the softened cream cheese, vanilla, and a pinch of salt, mixing well. Gradually add the sifted powdered sugar, one cup at a time, mixing on low speed until combined and thick.
Achieve Creamy Texture: Stir in the milk, one tablespoon at a time, beating on medium-high speed for about a minute until the frosting is light, fluffy, and perfectly spreadable.
Frost & Enjoy! Once the cake is completely cool, generously spread the delicious brown butter cream cheese frosting over the top. Swirl it artfully with a spoon or spatula. Optionally, sprinkle with extra cinnamon or nutmeg for a lovely finish.