1. To make frosting: In a medium saucepan, combine sugar, water, vanilla bean, and seeds. Cook over high heat, stirring, until sugar is dissolved. Using a wet pastry brush, wash down any crystals from side of pan. Cook over moderate heat without stirring until a medium-dark-amber caramel forms, about 9 minutes. Remove from heat and immediately stir in butter and heavy cream. (Don't worry if butter separates.) Discard vanilla bean.
2. Transfer caramel to large bowl of a standing mixer fitted with a whisk and beat at low speed until caramel cools slightly and comes together, about 5 minutes. With machine on, beat in cream cheese, 1 cube at a time and beating well between additions, until silky. Transfer frosting to a bowl and refrigerate until very firm, at least 6 hours.
3. Meanwhile, to make cake: Preheat oven to 350 degrees F. Butter and flour two 8-inch round cake pans. In a medium bowl, whisk flour with baking powder, salt, cinnamon, ginger, baking soda, nutmeg, and cloves.
4. In a bowl, using an electric mixer, beat brown sugar and eggs at medium-high speed until fluffy, 3 minutes. Beat in oil, then beat in pumpkin puree. Alternately add dry ingredients and milk in 3 batches, beating well between additions.
5. Pour batter into prepared pans and smooth tops. Bake 40 to 45 minutes, until a toothpick inserted in center of cake comes out clean. Let cakes cool on a rack 20 minutes. Run a knife around edges to loosen cakes, then invert onto a wire rack to cool completely.
6. Place 1 layer on a plate and spread with 1 cup caramel–cream cheese frosting. Put other half of pumpkin shaped layer together on first layer and frost remaining cake. Refrigerate cake 2 hours before serving.