How to Make It
Prepare the Caramel: Bring sugar, water, and corn syrup to a boil in a medium saucepan over medium, stirring once or twice. Continue to cook, without stirring, until mixture is a medium amber color, 8 to 9 minutes. Remove from heat, and immediately add heavy cream and butter (mixture will boil and foam). Whisk until well blended, and whisk in salt. Transfer to a bowl, cover with plastic wrap, and chill until cold, about 4 hours.
Meanwhile, prepare the Cake Layers: Place oven rack in center of oven; preheat oven to 350°F. Coat 2 (9-inch) round baking pans with cooking spray; lightly dust bottoms and sides of pans with flour.
Sift together flour, sugars, pumpkin pie spice, baking powder, baking soda, and salt in a large bowl. Whisk together pumpkin, buttermilk, oil, water, eggs, and vanilla in a medium bowl until well combined. Add pumpkin mixture to flour mixture; whisk gently until just blended but no lumps remain. Divide batter between prepared pans. Bake in preheated oven until a toothpick inserted in center comes out clean or with a few moist crumbs, 20 to 25 minutes. Cool Cake Layers in pans 20 minutes, and transfer from pans to a wire rack. Cool completely, about 1 hour.
Prepare the Frosting: Beat cream cheese in bowl of a stand mixer fitted with paddle attachment on low speed until softened, about 1 minute. Add butter and beat on medium speed until creamy, about 1 minute. Add powdered sugar, heavy cream, vanilla, and salt. Beat on low until incorporated; increase speed to medium until combined and thick but still spreadable, about 2 minutes. Chill 30 to 45 minutes before assembling cake.
Place 1 Cake Layer, top side up, on a cake plate. Dollop with about 1⁄2 cup of the Frosting, and spread evenly. Top with second Cake Layer, top side up, and dollop with another 1⁄2 cup of Frosting. Spread top and sides with a thin layer of Frosting. Chill 20 minutes. Take Caramel out of refrigerator, and let stand 20 minutes.
Generously swirl Caramel into remaining Frosting, keeping swirls large in mixture. Spread along top and sides of cake in a few swoops so it looks rustic. Chill 1 hour before slicing and serving.