Preheat oven to 350 degrees. In a large bowl, whisk together the pumpkin puree and eggs. Add brown sugar, oil, baking powder, cinnamon, baking soda, clove and nutmeg. Mix together. Add the flour and mix until well-combined.
Lightly grease a muffin pan or line with baking cups. Pour batter 2/3 of the way to the top of each cup. Bake 28-30 minutes. Allow to cool completely before frosting.
In a stand mixer fitted with the paddle attachment or in a large bowl with an electric hand mixer, beat the cream cheese, butter, maple extract and vanilla extract on medium-high speed for 1-2 minutes. Turn speed down to low and add the confectioner's sugar. Turn speed back up to medium-high and beat for another 1-2 minutes.