Preheat oven to 325˚F. Spray an 8-inch round cake pan with 2-inch sides. (If your 8-inch cake pan does not have 2-inch sides, use a 9-inch pan.) Line the pan with a round of parchment paper.
Add both sugars to the cooled melted butter and whisk to combine. Add eggs, pumpkin puree and vanilla, whisk again until well combined.
Sprinkle the flour, pumpkin pie spice, baking soda, baking powder and salt over the top of the wet ingredients. Whisk everything together until well combined and no lumps remain.
Transfer the batter into the prepared pan and smooth the top to level the surface. Bake for 45 to 50 minutes, or until a cake tester inserted into the center comes out clean. (Cover the top with foil during the last 10 minutes if it seems to be browning too much.)
Cool the cake for 10 minutes in the pan, then turn out onto a wire cooling rack to cool completely before icing.
For the icing:
Combine half and half, unwrapped caramels and brown sugar in a medium-size, microwave-safe bowl. Cook on high power for one minute. Remove from microwave and stir until smooth. If caramels are not completely melted, return to microwave for 15-second increments, stirring well in-between until completely melted and the mixture is nice and smooth.
Add vanilla and powdered sugar and soft butter and whisk well to combine. Continue whisking until the icing is smooth and spreadable. If it’s too thin add a bit more powdered sugar, if too thick and a teaspoon of half and half at a time until nice and spreadable.
Put a big dollop of frosting in the center of the cooled cake. Using an offset icing spatula, spread it to the edges and down the sides, adding more frosting to the top as you work your way around the cake. When the cake is completely iced, you can go back and add some swirls, if desired. Sprinkle with flaky sea salt and enjoy!
Notes
See Café Tips above in post for more details instructions and tips.