In a large mixing bowl, cream (or beat) together butter and sugar. Add eggs and vanilla until combined. Then, beat in pumpkin.
In another large bowl, combine all dry ingredients together until well combined.
Slowly add the dry ingredients to the wet ingredients and mix just until well combined.
Drop dough by spoonful on a lightly greased cookie sheet (or ungreased sheet with parchment). Bake in the preheated oven for 10 to 12 minutes or until tops are set. Transfer to a wire rack; let cool.
Frosting:
While the cookies bake and cool, prepare the frosting.
In a medium saucepan, heat the butter and brown sugar until melted and smooth. For richer caramel flavor, continue heating and stirring until the mixture comes to a boil.
Remove from heat, and stir in milk and vanilla.
Allow to the mixture to cool down (to about room temperature), then slowly beat in powdered sugar until desired consistency is reached. (I find that sifting the powdered sugar makes this frosting more smooth).
Spread frosting on cooled cookies. Sprinkle with cinnamon or sprinkles, if desired.