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1
Preheat the oven to 425u00b0F.
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2
Line a 12-cavity muffin pan with muffin/cupcake liners.
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3
Grate the carrots and finely chop the walnuts.
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4
Place the canola oil, brown sugar, 1/3 cup granulated sugar, eggs, applesauce, and 1 tsp. vanilla extract in a large mixing bowl. Whisk vigorously until smooth and combined.
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5
Add the flour, pumpkin pie spice, baking powder, baking soda, and salt to the bowl. Continue whisking until the mixture is just combined. Do not over-mix.
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6
Pro tip: Don't have pumpkin pie spice? Blend your own with a mixture of 9 parts cinnamon, 2 parts ginger powder, 2 parts nutmeg, 1 part allspice, and 1 part ground cloves.
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7
Fold in the grated carrots, raisins, and walnuts.
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8
Place the cream cheese, 2 Tbsp. granulated sugar, and 1/2 tsp. vanilla extract in a medium bowl. Beat with a mixer on medium speed for 2-3 minutes, until the mixture is completely smooth with no lumps.
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9
Add the egg yolk and beat on low speed until just combined.
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10
Fill each muffin cup about 1/4 of the way full. Spoon about a tablespoon of the cream cheese mixture into the center of each muffin. Cover the cream cheese mixture with more muffin batter, filling the cups no higher than 1/4-inch below the top edge. Repeat with the remaining carrot cake batter and cheesecake mixture.
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11
Bake the muffins at 425u00b0F for 5 minutes.
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12
Reduce the oven temperature to 350u00b0F. Continue baking for 14-16 minutes, or until a toothpick inserted in the center of a muffin comes out clean.
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13
Check to see that muffins are done. Remove from oven or add time as needed.
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14
Allow the muffins to cool in the pan for 5 minutes before removing. Refrigerate the muffins at least one hour before serving. Refrigerate leftovers in a container for up to 1 week.