Drain beets; reserve 3 tablespoons beet liquid. Cut whole beets in half. In small bowl, combine beet liquid, olive oil, mustard, garlic and salt and pepper, if desired. Whisk to blend. Stir in onion.
Toss beets with dressing-onion mixture. Refrigerate, covered, to chill. (Make up to one day in advance.) To serve, add broccoli. Toss gently to combine.