Add butter and powdered sugar to the bowl of a stand mixer. Beat with the paddle attachment until light and fluffy, about 2 minutes. Stir in vanilla extract.
Add instant espresso, cocoa powder, flour and salt to a medium bowl. Whisk together.
Gradually add the dry ingredients to the butter mixture. Stir until just combined. Add orange zest and stir until combined.
Form dough into 1 1/4-inch balls. Place on baking sheets lined with parchment paper or silicone mats.
Chill dough on the sheet pans in the refrigerator for 20 minutes.
When ready to bake, preheat oven to 400˚F. Bake for 10 to 12 minutes, until the edges of the cookies turn light brown.
Remove from oven and cool slightly.
Add powdered sugar to a medium bowl. While cookies are still warm, roll each one in the powdered sugar until coated.
Add to wire racks and cool completely.