Remove broccoli leaves and cut off tough ends of stalks; discard. Wash broccoli thoroughly and cut into flowerets. Blanch broccoli in boiling water 10 seconds. Plunge into ice water to stop cooking; drain well.
Combine broccoli, carrot, and cheese, tossing gently. Combine mayonnaise, sugar, and vinegar; stir well. Add mayonnaise mixture to broccoli mixture and toss gently.
Spoon broccoli mixture onto lettuce-lined salad plates, if desired, using a slotted spoon. Sprinkle with bacon and serve immediately.