Step 1

Adjust oven rack to lower-middle position and heat oven to 400 degrees. Generously spray inside of heavy-bottomed large (at least 7-quart) Dutch oven with nonstick cooking spray.

Step 2

Place butter in pot and add onions and 1 teaspoon salt. Cook, covered, 1 hour (onions will be moist and slightly reduced in volume).

Step 3

Remove pot from oven and stir onions, scraping bottom and sides of pot. Return pot to oven with lid slightly ajar and continue to cook until onions are very soft and golden brown, 1 1/2 to 1 3/4 hours longer,

Step 4

Place pot over medium-high heat. Cook onions, stirring frequently and scraping bottom and sides of pot, until liquid evaporates and onions brown, 15 to 20 minutes. Continue to cook, stirring frequently, until pot bottom is coated with dark crust, 6 to 8 minutes, adjusting heat as necessary. Stir in 1/4 cup water, scraping pot bottom and cook until water evaporates and pot bottom has formed another dark crust, 6 to 8 minutes. Repeat process 2 or 3 times, until onions are very dark brown. Stir in sherry and cook until sherry evaporates, about 5 minutes.

Step 5

Stir in broths, 2 cups water, thyme, bay leaf, salt, pepper, and paprika, scraping up any final bits of browned crust on bottom and sides of pot. Increase heat to high and bring to simmer. Reduce heat to low, cover, and simmer 30 minutes. Remove and discard herbs, then season with salt and pepper.

Step 6

Let soup cool completely then cover and refrigerate overnight. Remove from the refrigerator an hour before serving.

Step 7

Arrange baguette slices on baking sheet and bake in 400-degree oven until bread is dry, crisp, and golden at edges, about 10 minutes. Set aside.

Step 8

Heat soup to almost boiling. Adjust oven rack 6 inches from broiler element and heat broiler.

Step 9

Set individual broiler-safe crocks on baking sheet and fill each with about 1 3/4 cups soup. Top each bowl with 1 or 2 baguette slices (do not overlap slices) and sprinkle evenly with cheese.

Step 10

Broil until cheese is melted and bubbly around edges, 3 to 5 minutes. Let cool 5 minutes before serving.