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

Meanwhile, make the baguette toasts.

• Position a rack in the center of the oven and heat the oven to 350°F.
• 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.
• Set aside.

To Make the Soup

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

To serve

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