Preheat oven to 350°F (180°C). Line a 12-count muffin pan with paper liners.
In the bowl of a stand mixer fitted with the paddle attachment, cream butter, brown sugar, and granulated sugar together until slightly pale and fluffy, about 3-4 minutes.
Add eggs, finely grated carrots, and vegetable oil. Mix until well combined.
In another bowl, combine the flour, ground almonds, baking powder, baking soda, cinnamon, and salt. Add the flour mixture to the wet ingredients and mix until just combined.
Divide the batter between the muffin cups, fill each about 3/4 full, and bake for about 20 minutes or until a skewer comes out clean. Cool in the muffin pan several minutes then transfer to a wire rack and cool completely.
To make the frosting, beat together softened butter and powdered sugar in the bowl of a stand mixer fitted with the paddle attachment at medium speed until light and fluffy, about 2-3 minutes.
Add vanilla extract and cream cheese and beat until blended.
Frost cupcakes with cream cheese frosting.