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To make the frosting, add the cream cheese to the bowl of an electric stand mixer fitted with the paddle attachment. Whip on medium speed until light and fluffy, about three minutes.
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Scrape down the sides, add the butter, powdered sugar, brown sugar, vanilla, and salt. Mix slowly to combine. Then increase the speed to medium and beat until well combined. Transfer frosting to a separate mixing bowl and refrigerate until ready to use.
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Clean out the bowl of the mixer and the paddle attachment.
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To make the cupcakes, preheat the oven to 350 degrees F.
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Combine eggs, sugars, oil, and vanilla in the bowl of an electric stand mixer fitted with the paddle attachment. Mix on medium/low speed until eggs are broken up and combined.
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In a medium mixing bowl, whisk together the flour, baking powder, baking soda, salt, and cinnamon. Fold the flour into the sugar/egg mixture using a rubber spatula.
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Add the carrots and pistachios to the bowl, fold into the batter to combine.
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Add about 1/3 of a cup scoop of batter to each cavity in two muffin tins lined with paper cupcake liners. Bake in the oven for thirty minutes, until a toothpick inserted into the center of a cupcake comes out clean.
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Let the cupcakes cool on a wire rack for about ten minutes before frosting. Take the bowl of frosting out of the refrigerator to allow it to come to room temperature.
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When ready to frost, add the frosting to a piping bag or a large quart sized sealable plastic bag with one corner cut off. Pipe the frosting on to each cupcake. Top with a few extra chopped pistachios. Store cupcakes in an airtight container in the refrigerator for up to two days.