Transfer hot caramel to a large bowl and beat at low speed with an electric mixer until the caramel cools slightly and comes together, about 5 minutes.

With the mixer on, beat in the cream cheese, 1 cube at a time, beating well between additions until silky.

Taste the frosting and add additional powdered sugar for sweetness if desired.

Transfer the frosting to a bowl and refrigerate until very firm, about 90 minutes in the freezer or several hours in the fridge.

In a medium bowl, whisk together the flour, baking powder, salt, cinnamon, ginger, baking soda, nutmeg, and cloves.

In a large bowl, beat the brown sugar and eggs at medium-high speed until frothy and fluffy, about 3 minutes. Beat in the oil, then the pumpkin puree.

Alternately add the dry ingredients and milk in 3 batches, starting and ending with the flour, mixing until just combined.

Pour the batter into the prepared pans.

Bake at 350°F for 40 to 45 minutes, until a toothpick or knife inserted into the center comes out clean. Let cool in the pans for about 20 minutes.

Run a knife around the edges to loosen the cakes, then invert them onto a wire rack to cool completely.

Place one layer of cake on a plate and layer with frosting and cake. Drizzle with salted caramel sauce. Repeat with all layers.