Preheat oven to 350F. 12 muffin cups, greased or paper-lined. In a large bowl, whisk together sugar, pumpkin, oil and eggs until well blended.
In a small bowl, mix together flour, cinnamon, baking powder, baking soda, salt and ginger. Add flour mixture to pumpkin mixture and mix well. Spoon into prepared muffin cups, filling about three-quarters full.
Bake in preheated oven for 18 to 20 minutes, or until a toothpick inserted in center comes out clean and dry. Cool in pan for 10 minutes, then remove onto wire rack to cool completely.
Prepare frosting: In a small mixing bowl, beat cream and confectioners sugar until smooth. Add lemon zest and juice and continue to beat until smooth and blended. Swirl the tops of each cupcake with the frosting.