1. Melt the butter in a 4-quart pot over medium heat.
2. Stir in the onions and season with 1 tsp. salt and a few grinds of pepper.
3. Reduce the heat to low.
4. Cover the pot with a lid, and cook, stirring occasionally, until the onions are very soft but not falling apart, 40 to 50 minutes.
5. Remove the lid raise the heat to medium high,cook, stirring often, until browned, about 10 minutes.

Meanwhile, make the baguette toasts.

1. Position a rack in the center of the oven and heat the oven to 350°F.
2. Butter a rimmed baking sheet and arrange the baguette slices on the sheet in a single layer. Bake until the bread is crisp and lightly browned, turning once, 15 to 20 minutes.
3. Set aside.

To Make the Soup

1. Add the broth and bay leaf to the caramelized onions and bring the soup to a boil over medium-high heat.
2. Reduce the heat to medium low and simmer for 10 minutes to blend the flavors.
3. Discard the bay leaf and season to taste with salt and pepper.

To serve

1. Position a rack 6 inches from the broiler and heat the broiler to high.
2. Put 6 to 8 broiler proof crocks on a baking sheet.
3. Put 2 or 3 toasts in each bowl and ladle the hot soup on top.
4. Sprinkle with the cheese and broil until the top is browned and bubbly, 2 to 5 minutes.
5. Serve immediately.