Mix together sugars and butter, then add pumpkin, egg, and vanilla and continue to mix.
Add remaining dry ingredients and mix until combined.
Drop spoonfuls of pumpkin cookie batter onto non-greased cookie sheet
Bake at 350 degrees for 10-12 minutes.
Maple Frosting:
Boil 3 Tbsp butter and 1/2 C brown sugar until mostly smooth (Approx. 2 to 3 minutes)
Cool and add 1/4 C milk and 2 C powdered sugar or until desired consistency and whip with hand mixer until smooth
Spread onto cookies
Notes
To make your own pumpkin pie spice combine: 1 1/2 tbsp. cinnamon 1 tsp ground ginger 1 tsp nutmeg 3/4 tsp ground allspice 3/4 tsp ground cloves Use 1/2 tsp for this recipe and then save the rest for later.