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Preheat oven to 350 degrees. Spray three 8x8 inch square pans or two 9 inch square pans with nonstick cooking spray.
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In a bowl, sift together flour, baking powder and soda, salt, cinnamon, and pumpkin pie spice.
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In the bowl of your mixer, beat oil, sugar, and vanilla until it is fully incorporated.
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Add pumpkin puree and mix to combine.
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Beat in eggs, one at a time, scraping down the bowl after each addition.
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Gradually add flour to the pumpkin mixer, mixing on low and until just combined.
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Evenly distribute batter into pans and bake for 25-30 minutes, or until a knife is inserted and comes out clean, depending the your oven and the size of the pans.
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Allow cakes to cool completely before frosting.
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To make the frosting beat together cream cheese, butter, vanilla and salt.
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Slowly add in powdered sugar then increase mixer speed to high and beat for 4-5 minutes.
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To assemble the cake, spread about ⅓ cup of dulce de leche onto first layer, then top with about 1 cup of frosting.
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Add next layer and repeat process.
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For the final layer, spoon remaining frosting into a a pastry bag fitted with a large tip.
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Pipe frosting and sprinkle with pumpkin pie spice.