Preheat the oven to 350℉ (177℃). Line three 8-inch cake pans with parchment paper circles on the bottom and spray with baking spray.
In a large mixing bowl, combing the flour, granulated sugar, brown sugar, baking powder, baking soda, salt, cinnamon, nutmeg, ginger, and cloves. Mix on low speed or whisk until the spices are evenly dispersed.
2 3/4 cups (388g) all-purpose flour, 1 1/2 cups (300g) granulated sugar, 1/2 cup (100g) packed brown sugar, 2 1/2 teaspoons baking powder, 1/2 teaspoon baking soda, 1/2 teaspoon salt, 2 teaspoons ground cinnamon, 1 teaspoon ground nutmeg, 1/2 teaspoon ground ginger, 1/4 teaspoon ground cloves
With the mixer running on medium-low speed, add the softened butter one tablespoon at a time, mixing for 20-30 seconds after each addition. Once all of the butter has been added, add the oil and beat for 1-2 minutes until light.
3/4 cup (170g) salted butter, 1/4 cup vegetable oil
Add the pumpkin, eggs, milk, and vanilla. Beat again until smooth and completely combined, stopping to scrape the bottom and sides of the bowl.
1 (15-ounce) can pumpkin puree, 3 large eggs, 1/2 cup milk, 2 teaspoons pure vanilla extract
Divide the batter evenly between the prepared cake pans. Bake for 30 to 35 minutes or just until a toothpick or tester inserted into the center of each cake comes out clean with just a few moist crumbs clinging to it. Cool completely on a wire rack.
To make the frosting, beat the butter and cream cheese together in a large mixing bowl until completely combined and smooth. Add the powdered sugar, cinnamon, and vanilla, then mix just until smooth and combined. It should be light, fluffy, and spreadable, but do not overmix or the frosting can become runny. If the frosting seems thin, try refrigerating it for 30-60 minutes to firm up a bit.
1 cup (227g) salted butter, 8 ounces full-fat cream cheese, 5 cups (600g) powdered sugar, 2 teaspoons ground cinnamon, 2 teaspoons pure vanilla extract
To assemble, level off any domed tops so the cake layers are flat and even. Stack the layers on a decorative cake stand or plate with a generous amount of frosting between each layer. Seal in the crumbs with a very thin layer of frosting around the top and sides, then freeze the whole cake for 30 minutes to help set the frosting. This is important since cream cheese frosting is softer than other types of frosting and this helps make the cake much easier to finish decorating. Once thoroughly chilled, use the remaining frosting to frost the outside of the cake before slicing and serving.