Cook potatoes in a large saucepan of boiling water, 15 minutes until fork tender, adding broccoli in last 2 minutes of cooking. Drain well. Return to pan; mash until desired consistency.
Add soup, 1 cup (250 mL) of the cheese, eggs, mustard, thyme, salt, pepper (optional) and parsley (optional). Mix well; scrape into 3 qt (2.85 L) baking dish. Sprinkle with remaining cheese.
Bake 40 minutes or until golden and slightly puffed.