Heat espresso and 1/4 cup sugar in a small saucepan and bring to a boil. Simmer until mixture has reduced to a thick syrup, 12 to 15 minutes. Remove from heat and allow to cool for 30 minutes.
Preheat the oven to 350 degrees F (175 degrees C). Line 2 baking sheets with parchment paper.
Combine butter, 3/4 cup sugar, and egg in a bowl; beat using an electric mixer until light and fluffy. Mix in vanilla extract, baking powder, and baking soda until well combined. Mix in cooled espresso syrup. Add flour and mix until blended. Fold in cacao nibs.
Scoop 2 tablespoons dough per cookie onto the prepared baking sheets, leaving 2 inches of space between each for about 12 cookies per sheet.
Bake 1 baking sheet with cookies in the preheated oven for 10 to 12 minutes. Repeat with the second baking sheet.