In a mixing bowl, beat butter with white and brown sugar until creamy. Add egg and mix until incorporated. Stir in espresso until fully combined. Add flour, baking powder, and baking soda; mix until dough forms. Chill for 30 minutes.
Scoop dough with an ice cream scoop onto a parchment-lined baking sheet, spacing cookies evenly. Bake for 12 minutes. Cool completely on a wire rack.
Whip cream with powdered sugar until soft peaks form. Fold in vanilla pudding powder until smooth. Pipe cream in spirals atop each cooled cookie. Dust with cocoa powder and serve.