Place popcorn in a large bowl that has been sprayed with cooking spray; set aside. Line a baking sheet or work surface with waxed paper or foil.
Stir sugar, cocoa, instant coffee and milk together in a large saucepan. Cook until mixture registers 250 on a candy thermometer, stirring occasionally.
Pour hot mixture over popcorn; stir to coat popcorn completely. Spread popcorn onto prepared surface and allow to cool. Sprinkle with powdered sugar. Break into pieces to serve. Store in an airtight container.