Heat to 350°F.
Butter two 9-inch round cake pans and line the bottom with rounds of parchment paper. Butter the parchment paper, as well, then flour the parchment paper bottom and sides of the pan.
Sift together flour, baking powder, baking soda, salt, cinnamon, ginger, nutmeg, and cloves.
In the bowl of a stand mixer (or in a large bowl, using a hand mixer), beat on medium speed granulated sugar, brown sugar, and butter until fluffy, about 3 minutes. Beat in eggs one at a time. Stir in pumpkin and vanilla until just combined (low speed on the mixer).
Add the flour/spice mixture to the butter/sugar/eggs mixture, stirring until just combined.
Divide the batter between the buttered pans. Lightly tap the pans on the countertop and smooth out the tops of the batter.
Bake until cakes pull away from sides of pan, start to barely turn golden at the edges, and a toothpick inserted into the center of a cake comes out clean, about 35 minutes. Cool the baked cakes for 15 minutes in their pans. Flip the cakes onto wire cooling racks and peel off the parchment paper. Let cool completely (upside down, so the rounded tops can flatten out a little).
You can bake the layers a day in advance, let them cool, wrap them up tightly in plastic wrap and keep in the refrigerator.
Make the Cream Cheese Frosting while the cake layers are baking.