Preheat oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a bowl, whisk together flour, cocoa powder, baking powder, salt, and espresso powder.
In another bowl, beat butter and sugar until fluffy.
Add the egg and vanilla, mixing until combined.
Gradually incorporate dry ingredients, alternating with milk, until a soft dough forms.
Scoop tablespoon-sized portions and roll them into balls.
Place cookies on the baking sheet, 2 inches apart.
Use your thumb or a spoon to make a small indent in the center of each.
Bake for 10-12 minutes, until edges are set but centers are soft.
Let cool for 5 minutes, then fill the indentations with melted chocolate.
Allow chocolate to set or just eat them immediately (no judgment).