Add the melted butter, granulated sugar, and brown sugar to a large bowl. Mix to combine.
In a small bowl, stir the espresso powder and 1 tablespoon of hot water together until a smooth paste forms.
Add the espresso paste to the butter and sugar mixture and stir until evenly incorporated with no streaks.
Add the egg and vanilla to the mixture and stir until fully combined.
Add the flour, baking powder, baking soda, and salt. Mix until a soft dough forms with no dry pockets of flour.
Fold in the dark chocolate chips.
Cover and chill the dough for 30 minutes, until firm enough to scoop cleanly.
Towards the end of the chilling period, preheat the oven to 350 F.
Scoop roughly 1 ½ tablespoon portions of dough and roll into balls. Place the dough balls onto the prepared cookie sheets, leaving about 2 inches between each one to allow space for spreading.
Bake the cookies for 12 minutes, until the edges are set and the tops look slightly puffed but still soft.
Let the cookies rest on the baking sheets for at least 10 minutes, until firm enough to lift without bending.
Transfer the cookies to a wire rack to cool completely before serving.