Start by combining all of the chai spice ingredients in a small bowl and set aside.
Add the stick of butter, coconut oil, brown sugar, and coconut sugar to a large bowl. Using a mixer, beat until well combined.
Beat in the pumpkin, egg, and vanilla.
Slowly add the flour, 1 tbsp. of the chai spice, and the baking soda until everything is well combined.
Stick the dough in the refrigerator for 30 minutes and line a baking sheet with parchment paper. In a small bowl, combine the cinnamon and sugar mixture.
Once the dough comes out of the refrigerator, roll into 1 tablespoon sized balls. Run them through the cinnamon-sugar mixture and place on the baking sheet. You might have to flour your hands. The dough should be a little sticky. Gently flatten each dough ball until they are about 3/4 of an inch thick.
Bake at 350 degrees for 11-13 minutes.
To prepare the icing, add the coffee grounds to 1 tbsp. plus 1 tsp. of warm water. Using a mixer, beat togeher the cream cheese and butter for 2-3 minutes. Add the sugar, vanilla, and coffee. Beat until everything is well combined and the icing looks fluffy. If you want a stronger coffee flavor, combine the coffee grounds with only 1 tbsp. of warm water.
Once the cookies have cooled, top them with the icing and sprinkle on a little bit of the remaining chai spice.