Preheat oven to 350°F (175°C). Line a 12-cup muffin pan with cupcake liners.
Combine wet ingredients: Mix pumpkin puree, sugar, oil, eggs, and vanilla in a bowl.
Mix dry ingredients: In a separate bowl, combine flour, baking powder, baking soda, salt, cinnamon, nutmeg, and cloves.
Combine mixtures: Fold dry ingredients into the wet mixture until just combined.
Fill liners: Divide batter among cupcake liners, filling each about 2/3 full.
Bake for 18-22 minutes. Cool completely on a rack.
Prepare frosting: Beat cream cheese and butter until smooth. Gradually add powdered sugar, then mix in vanilla and cinnamon.