Preheat oven to 375 degrees. Line 2 baking sheets with parchment paper.

In a small mixing bowl, whisk together flour, baking powder, soda, cinnamon, nutmeg, cloves, and salt.

In the bowl of an electric mixer, cream together butter and sugar until fluffy. Add pumpkin and beat until smooth. Add the flour mixture to the pumpkin mixture and beat on low speed until the mixture is well combined and cohesive.

Scoop mounded Tablespoons of dough onto the cookie sheet. These don't spread much so you can keep them fairly close together. Bake for 9-10 minutes, or until tops are firm to the touch. (Your finger shouldn't leave an indent when the tops are lightly touched).

Remove from heat and allow to cool for a few minutes on the baking sheet then cool completely on a wire rack.

Melt butter in a small saucepan. Add brown sugar and bring mixture to a boil. Reduce heat to a simmer and simmer for 2 minutes, stirring constantly. Add milk or cream and salt, return mixture to a boil, then remove from heat. Allow to cool slightly, then whisk in vanilla.

Whisk in 1/2 cup powdered sugar until smooth. Continue to add additional powdered sugar until mixture is thick, but spreadable. It should be considerably thinner than normal frosting. I like it to be at a thickness that allows me to spoon the mixture on then spread it with a spoon or metal icing spatula.

Frost cookies while frosting is still warm. The frosting will harden and thicken as it cools. If the frosting becomes too thick to spread while frosting the cookies, you can return it to heat for a few minutes or add a few Tablespoons hot water.