Preheat oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a bowl, whisk together flour, baking powder, salt, and espresso powder.
In another bowl, beat butter and sugar until fluffy.
Add egg and vanilla extract, mixing until smooth.
Gradually incorporate the dry ingredients, alternating with milk, until a soft dough forms.
Scoop tablespoon-sized portions onto the baking sheet, spacing 2 inches apart.
Flatten slightly with the back of a spoon.
Bake for 12 minutes, or until the edges turn golden.
Let cool on the baking sheet for 5 minutes, then transfer to a rack.
Eat immediately, or store in an airtight container (if they last that long).