Preheat the oven to 350℉.

In a large mixing bowl, with the paddle attachment, beat the sugars and butter until well-creamed. Add the eggs, pumpkin, and vanilla and mix well.

Add the remaining ingredients and mix to combine.

Scoop onto greased cookie sheets and bake for 11 - 13 minutes or until the edges are firm. Remove to a wire rack to cool.

Spread the cookie tops with frosting and store them in an airtight container with parchment paper between the layers.

Keep at room temperature for up to two days, in the refrigerator for up to a week, or frozen in an airtight container for up to 2 months.

Melt the butter in a saucepan. Add the brown sugar and boil over medium/low heat for 2 minutes, whisking occasionally.

Add the milk and salt. Whisk until it comes back to a full boil.

Remove from the heat and cool to lukewarm. Beat in the powdered sugar until smooth. Spread on the cooled cookies.