Preheat oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a bowl, whisk flour, baking powder, salt, and espresso powder.
In another bowl, beat butter and sugar until fluffy.
Add the egg and vanilla, mixing until combined.
Gradually add dry ingredients, alternating with milk, until a soft dough forms.
Roll dough into a ¼-inch thick rectangle on a floured surface.
Brush melted butter over the dough.
Mix brown sugar and cinnamon, then sprinkle over the buttered dough.
Roll dough tightly into a log, then slice into ½-inch rounds.
Place cookies 2 inches apart on the baking sheet.
Bake for 10-12 minutes, until edges are golden.
Let cookies cool on a rack while you prepare the glaze.
Whisk powdered sugar with brewed coffee until smooth.
Drizzle glaze over cooled cookies.
Let the glaze set—or don’t, and eat immediately.