Preheat oven to 350.
Spray a 12-cup cupcake pan with cooking spray and line with paper liners; set aside.
In a medium mixing bowl, whisk together flour, baking powder, baking soda, salt, cinnamon and nutmeg; set aside.
In a large mixing bowl, whisk together eggs, pumpkin puree, sugar, oil, and vanilla.
Slowly whisk in the flour mixture to the pumpkin mixture; stir until well combined.
Pour batter into prepared cups, filling each cup 3/4 full.
Bake for 30 to 35 minutes, or until a toothpick inserted in the center comes out clean.
Cool in pan 5 minutes; transfer cupcakes to a wire rack to cool completely.