Cream together the butter and sugar until fluffy, about 3-4 minutes. Add in the chai concentrate and cream again. It might not fully emulsify, but don't sweat it.
In another bowl, whisk together the flour, cornstarch, baking powder and salt.
Gradually add your dry ingredients to the wet ingredients until a batter forms. If you want your chai “dirty,” fold in 1 tsp of instant coffee or espresso powder.
Chill the dough in the freezer while you preheat your oven to 400F.
Make an icing by whisking together the powdered sugar, brewed coffee and instant coffee or espresso powder.
Form the dough into 9 equal sized balls, place on a parchment lined baking sheet and make a small indent in the middle of each cookie. This will help them spread evenly.
Bake at 400F for 12-15 minutes.
Place them on a cooling rack to fully cool, then top with the icing in the middle of the cookie!
Store in an airtight container at room temperature for up to 5 days.