Vegetarian French Onion Soup

This recipe comes from Mark Bittman's How to Cook Everything Vegetarian.

Ingredients
1/4 cup extra virgin olive oil or 4 tbs (1/2 stick) butter
4 large onions, thinly sliced (about 6 cups)
Leaves of 2 or 3 sprigs fresh thyme or 1/4 tsp dried
1 bay leaf
1 whole head garlic, cut crosswise through the equator
Salt and freshly ground black papper
5 cups vegetable stock
2 tbs cognac, Armagnac, or brandy (optional)
2 tbs parsley leaves, or more to taste, for garnish (optional)
1 cup freshly grated Parmesan
4 thick slices crusty bread

Directions

1. Put oil or butter in a large, deep saucepan or casserole over medium heat.  When the oil is hot or the butter is melted, add the onions and cook, stirring occasionally, until very soft and beginning to brown. This will take 30 to 45 minutes; don't rush it.

2. Add the thyme, bay leaf, garlic, and salt and pepper to taste and cook with the onions for a minute before adding the stock and cognac (if you have parsley, add a few sprigs to the soup at this point; fish them out before serving). Bring to a boil, then turn the heat to medium-low and cook for 15 minutes, with bubbles occasionally breaking the surface.  (You may prepare the soup in advance up to this point; cover and refrigerate for up to 2 days, then reheat before proceeding.)

3. Preheat the oven to 400 degrees F. Cut 4 thick slices of crusty bread, rub them with a clove of garlic on each side, and toast them in the oven, in a toaster oven, or in a pan with olive oil (a la croutons).  Put a crouton in each of 4 ovenproof bowls.  Add a portion of soup and top each with at least 1/ cup of freshly grated Parmesan cheese.  Place the bowls in a roasting pan or on a sturdy cookie sheet and bake for 10 minutes, or until the cheese melts. Serve immediately.