Preheat the oven to 375 degrees F (190 degrees C). Line 2 baking sheets with parchment paper.

Combine butter, brown sugar, 1/3 cup sugar, and coffee powder in a large bowl; beat with an electric mixer until creamy. Blend in eggs and vanilla extract. Mix in flour, cocoa powder, baking soda, and salt together until dough is uniform.

Pour 1/2 cup sugar onto a shallow plate. Shape dough into 2-inch balls and roll in the sugar until coated. Arrange on the prepared baking sheets.

Bake in the preheated oven until edges are set, about 10 minutes. Immediately press a dark chocolate wafer into each cookie. Let cool on a wire rack.