Peel and cut onions in wedges. Place in large bowl. Combine lemon juice, mustard, garlic, thyme, salt and pepper in a small bowl. Whisk in the olive oil. Pour all over the onions, toss well.
With a slotted spoon, put onions on a sheet pan. Save vinaigrette in the bowl. Bake onions for 30 to 45 minutes until tender and browned. Toss once during cooking. Remove from oven & drizzle the remaining dressing. Sprinkle with parsley. Season to taste and serve warm or at room temperature.