Step 1

Position racks in the upper and lower thirds of the oven; preheat to 350 degrees F. Line 2 baking sheets with parchment paper. Coarsely grind the coffee beans in a coffee grinder. Combine 1 tablespoon ground coffee in a small bowl with the turbinado sugar; set aside. Transfer the remaining coffee to a medium bowl and whisk in the flour, salt, baking powder and cinnamon.

Step 2

Beat the butter and brown sugar in a large bowl with a mixer on medium-high speed until light and fluffy, about 3 minutes. Beat in the egg. Reduce the mixer speed to low and beat in the flour mixture until combined.

Step 3

Roll tablespoonfuls of dough into balls, then roll each ball in the coffee-sugar mixture. Arrange 2 inches apart on the prepared pans.

Step 4

Bake, switching the pans halfway through, until the cookies are just set around the edges but the centers are still soft, about 18 minutes. Let cool 3 minutes on the pans, then transfer to racks to cool completely.

Step 5

Make the glaze: Whisk the confectioners' sugar and 2 teaspoons milk in a small bowl until smooth. Gradually stir in up to 2 more teaspoons milk until the glaze is thick but pourable. Spoon the glaze over the cookies. Let set, about 10 minutes.