Preheat oven to 375ºF. In a large mixing bowl, cream butter and sugars together using a hand mixer/kitchen aid on medium speed until the mixture is smooth.
Add eggs, vanilla, salt, and baking soda to the butter mixture. Add pumpkin puree and pumpkin pie spice. Mix on medium speed only until ingredients are blended and smooth.
Dissolve 2 tsp instant coffee in cold milk, per the instructions on the can, and add this to the bowl. Mix well.
Add flour. Mix on low speed until flour is no longer loose, and medium speed only until flour is blended fully. (Add Tbsp extra flour if dough seems too sticky after this step, and mix on low speed only for a few seconds.)
Finally add remaining 1 Tbsp instant coffee bits until evenly mixed in the dough. Do not overmix.
Line a cookie sheet with parchment paper. Scoop cookie dough using a medium-sized cookie scooper slightly rounded, and place at least 2" apart onto cookie sheet (approx. 1¾ Tbsp of dough for each cookie).
Bake at 375ºF for 9-11 minutes, taking out when tops are still light but edges are brown.
Slide parchment paper with cookies off the baking sheet directly onto the counter for cooling. (If not using parchment paper, let cookies sit for one minute and then remove to cool on the counter or wire rack.)
Top the cookies with sifted powdered sugar and serve.
