Roast beets: Wash beets and place in tin foil. Bake in 400 oven for 45 - 1 hour (depending on size). Test beets with a fork to see if cooked inside. Remove and let cool slightly. Peel and set aside. (can be done in advance).
Vinaigrette: Combine shallots, balsamic vinegar, olive oil and grainy mustard. Salt and pepper to taste. (can be done in advance).
In a bowl, add just enough dressing to coat lettuce leaves. Divide salad on plates, top with red onion and sprinkle with goat cheese.