Preheat oven to 350 F and grease or line with paper cups 24 muffin cups.
Cream butter and sugars until evenly combined. Add eggs one at a time, beating well after each addition. Stir in pumpkin, sour cream and vanilla. In a separate bowl, sift flour, baking powder, baking soda, salt and spices. Stir into pumpkin mixture, then stir in grated carrots. Spoon into prepared tins and bake for about 25 minutes, until a tester inserted in the centre of the muffin comes out clean. Cool for 15 minutes in the tin before removing to cool completely.
For frosting, beat butter with electric beaters until fluffy. Add 2 cups of icing sugar, plus milk and vanilla and beat for 3 minutes on high speed until fluffy. Add remaining 1 to 2 cups icing sugar until frosting is a fluffy, spreadable consistency. Spread frosting generously onto each muffin.