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Preheat the oven to 350°F. Grease two 8” round cake pans; line with parchment, and grease the parchment.
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To make the cake: In a large bowl, whisk together the sugar, flour, salt, baking powder, baking soda, and pumpkin pie spice.
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In a separate medium-sized bowl, whisk together the eggs, buttermilk, pumpkin, oil, vanilla, and water.
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Add the wet ingredients to the dry ingredients, stirring to combine. Pour the batter into the cake pans.
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Bake the cakes for about 35 to 38 minutes, until a toothpick inserted into the center of one comes out clean.
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Remove the cakes from the oven and let them cool in the pans for 10 minutes. Turn them out onto a rack to cool completely.
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To make the frosting: Using an electric or stand mixer, beat together the butter and cream cheese at medium-low speed until smooth.
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Gradually add the confectioners' sugar, beating to combine.
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Beat in the extracts and salt.
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To assemble the cake: When the layers are completely cool, level their tops (either both layers, or just the bottom layer).
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Place the bottom layer on a serving plate. Frost it, then add the top layer. Frost all over with an offset spatula.
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If you’re garnishing with the caramel, freeze the cake until the frosting is solid and cold.
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About 2 hours before serving, melt the caramel on the stove or in the microwave, and stir it for a bit to cool it slightly; you want it pourable, but not so hot that it'll melt the frosting.
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Pour the caramel over the cake; it should ooze very slowly down the sides of the cake, taking about 90 minutes to do so. Serve the cake within an hour or so after that; letting it sit any longer causes the caramel to begin to puddle at the base of the cake.
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Garnish with coarse sea salt, just before serving.
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Store any leftover cake, well-wrapped, in the refrigerator for a day or so; freeze for longer storage.