To make cupcakes: Blend the eggs, oil, sugar, and pumpkin in a large mixing bowl; set aside. Stir together dry ingredients in a separate bowl. Add dry ingredients to pumpkin mixture and beat until well blended.
Pour into lined muffin tins. Fill about 2/3 full. Bake in preheated 350°oven for 30 minutes or until center springs back when touched. Cool 30 minutes. Spread with frosting.
To make frosting:
Beat cream cheese and butter until fluffy. Add remaining ingredients and beat until smooth. Spread over cooled cupcakes.