Preheat the oven to 350°F. Lightly grease or line a 12-cup muffin tin.
In a large bowl, whisk together the ¾ cup vegetable oil, 1 cup granulated sugar, and 2 large eggs.
In a medium bowl, whisk the 1 cup oat flour with the ¾ teaspoon baking powder and ¼ teaspoon baking soda, ½ teaspoon fine sea salt, and spices. Stir this mix into the wet ingredients. Fold in the 1 ½ cups shredded carrots.
Divide the batter equally among the muffin cups and let it rest for up to 20 minutes. Place the pan in the oven and bake for about 25-30 minutes until a tester comes out clean. Cool in the pan for 5 minutes, then turn out the cupcakes to cool completely.
Make the frosting
In a large bowl, cream the ½ cup unsalted butter and cream 8 ounces cream cheese until light and fluffy. Gradually beat in the 3-4 cups powdered sugar until it reaches your desired consistency and sweetness.
Frost the tops of the cupcakes.
Notes
Refrigerate the cupcakes before frosting. At room temperature, the cupcakes are fairly soft. To help them hold together when you add the frosting, chill the cupcakes for about 30 minutes in the fridge. Make sure to use a gentle hand when adding the frosting.
Add other spices. You can add ¼ teaspoon each of ground nutmeg and cardamom to give the cupcakes a more deeply spiced flavor.
Stir in nuts. For a little crunch to offset the softness of the cupcakes, add ½ cup of chopped walnuts to the batter when you add the carrots.
To make refined sugar-free: Use ⅔ cup of maple syrup or coconut sugar instead of the granulated sugar.
To make dairy-free: Substitute your favorite non-dairy butter and non-dairy cream cheese in the frosting.
Frosting alternatives. You can add a simple vanilla buttercream frosting to the cupcakes if you don't care for cream cheese frosting. Or sift a little powdered sugar over the tops of the cakes for a simple finish.
Add maple syrup. For a touch of maple flavor in the frosting, add a little maple syrup, 1 teaspoon at a time, when you add the powdered sugar.