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 Cream Cheese Frosting ~ 10 minutes
Make the Cream Cheese Frosting while the cake layers are baking: beat together cream cheese, butter, vanilla, and sea salt until smooth with an electric hand mixer or in a stand mixer with the the beater attachment.
Gradually add confectioner's sugar about ¼ cup at a time until the cream cheese and butter have the consistency of a thin frosting. You will need 2-3 cups, depending on how warm your kitchen is.
Keep the frosting covered and in the refrigerator until the cake is ready for assembly.
Make Caramel Sauce ~ 7 minutes
In a medium stainless steel or light-colored pot over medium/low heat, melt sugar, swirling pan and stirring occasionally with a metal or silicone spatula.
Once the sugar is fully melted and turns a light amber color, immediately remove the pot from heat and stir in butter, taking precautions, as the mixture may bubble and spurt. Stir together until the butter has melted and combined with the sugar completely.
Slowly add the heavy cream, gently stirring until everything is combined. You may need to return the pot to the stove for 20-30 seconds to keep the caramel smooth.
Remove the pot from the heat completely. Stir in salt. Cool to room temperature in the pot or a heat-proof (glass) container before using.
Cake Assembly
Carefully slice cooled cake layers across the “equator” into two halves each. Brush away any errant crumbs. Place one layer on a cake stand or plate — I’ve had better luck when I place layers with the flat, cut side down.
Top the bottom later with enough frosting to make a ½-inch thick layer of frosting.
Add a second layer. Top the second layer with a ½-inch thick layer of frosting. Add the third layer, frost, and finally add the fourth layer. Frost the tops and sides of the cake. Try to frost the top as flat and level as possible so the caramel doesn’t run off too easily.
Drizzle caramel sauce over the top of the cake an . You can also leave the cake frosted as is and drizzle caramel sauce on each piece of cake on individual plates.