To begin, preheat your oven to 350 and spray two pans with non-stick spray (or line with parchment paper).
To a large mixing bowl, add your butter and brown sugar and beat them together with a mixer till creamy. Add your pumpkin puree and vanilla and mix in until well combined. Add your egg and lightly mix it in.
To the same bowl, add your flour, baking soda, salt, and pumpkin pie spice. Stir till well combined and you have a thick, smooth cookie batter.
Using a cookie scoop, scoop the dough onto your pans evenly spaced apart, for no more than 12 cookies per pan. Bake in the oven for 12-14 minutes, or till the edges are just starting to turn golden brown and the top has set.
Let cool entirely before frosting the cookie tops.
Heat 2 tbsp of milk till warm. Add your instant coffee and whisk till combined.
To a large mixing bowl, add your butter, 2 tbsp of milk and coffee, powdered sugar, and vanilla. Beat with a mixer, starting on low, and working your way up to high. Beat till you have a smooth and even frosting. If your frosting is too firm, add another 1/2-1 tbsp of milk.
Spread onto the tops of your cooled cookies. Add sprinkles for fun!
Devour!
I recommend storing these cookies in an airtight container in the fridge, due to the pumpkin and frosting. Stored this way, they will last about a week.