Carrot Cake Cupcakes

Name: Carrot Cake Cupcakes
Ingredients: 1 3/4 c. all-purpose flour; 1/2 tsp. baking soda; 1/2 tsp. baking powder; 1/2 tsp. ground cinnamon; 1/4 tsp. kosher salt; 1/4 tsp. ground ginger; 1/8 tsp. ground nutmeg; 2 Sticks unsalted butter, softened; 2/3 c. firmly packed light-brown sugar; 1/2 c. granulated sugar; 2 large eggs, preferably at room temperature; 1 1/4 tsp. vanilla extract; 1/3 c. milk; 1 1/2 c. loosely packed carrots, shredded on the small side of the box grater; Half a carrot, for garnish; Cream Cheese Frosting (recipe link in step 6); Raw walnut halves, for garnish