Melt butter in heavy, large sauce pan over medium heat.

Add onions, garlic, bay leaf and thyme spring and saute until very tender and brown, about 25 minutes.

Add 1/4 cup wine to deglaze pot every 5 minutes for 20 minutes (total onion cooking time is 45 minutes).

Stir in Dijon mustard.

Add white wine and simmer until reduced to a syrup consistency, about 3 minutes.

Stir in vegetable stock. Simmer 20 minutes.

Season to taste with salt and pepper.

--------------- To assemble --------------------

Preheat broiler.

Ladle soup into overproof bowls.

Top each with slice of toast and grated cheese.

Broil until cheeses melt and bubble.