Preheat oven to 350°.
Place 1 phyllo shell into each of 36 miniature muffin cups.
Combine coffee granules, hot water, and Kahlúa in a small bowl. Place coffee mixture, sugar, and the next 5 ingredients (sugar through egg) in a food processor; process until smooth. Spoon about 1 tablespoon cheese mixture into each shell; discard the remaining filling. Sprinkle cheesecakes evenly with toffee bits.
Bake at 350° for 15 minutes or until set. Remove from pans, and cool on a wire rack.