Cut a piece of cheesecloth about 7 inches square. Place the bay leaves, peppercorns, and thyme in the center, bring up the edges, and tie with kitchen twine to form a sachet. You may also use a metal tea-ball or anything that will allow you to remove the aromatics from the finished soup.

Cut off the tops and bottoms of the onions, then cut the onions lengthwise in half. Remove the peels and tough outer layers. Cut a V wedge in each one to remove the core and pull out any solid, flat pieces of onion running up from the core. Lay an onion half cut side down on a cutting board with the root end toward you. Note that there are lines on the outside of the onion. Cutting on the lines (with the grain) rather than against them will help the onions soften. Holding the knife on an angle, almost parallel to the board, cut the onion lengthwise into 1/4 inch thick slices. Once you’ve cut past the center of the onion, the knife angle will become awkward: Flip the onion onto its side, toward the knife, and finish slicing it, again along the grain. Separate the slices of onion, trimming away any root sections that are still attached and holding the slices together. Repeat with the remaining onions. (You should have a lot of sliced onions, about 7 quarts.)

Melt the butter in a large heavy stockpot over medium heat. Add the onions and 1 tablespoon salt, reduce the heat to low. Cook, stirring every 15 minutes and regulating the heat to keep the mixture bubbling gently, for about 1 hour, or until the onions have wilted and released a lot of liquid. At this point, you can turn up the heat slightly to reduce the liquid, but it is important to continue to cook the onions slowly to develop maximum flavor and keep them from scorching. Continue to stir the onions every 15 minutes, being sure to scrape the bottom and get in the corners of the pot, for about 4 hours more, or until the onions are caramelized throughout and a rich deep brown. (Very dark brown, not burned, sweet and rich in taste.) Keep a closer eye on the onions toward the end of the cooking when the liquid has evaporated. They will burn easily at that stage. (I have “tested” this.) Remove from the heat. (You will need 1 1/2 cups of caramelized onions for the soup; reserve any extra for another use. The onions can be made up to 2 days ahead and refrigerated.)

Transfer 1 1/2 cups of the caramelized onions to a 5 quart pot (if they’ve been refrigerated, reheat until hot.) Sift in the flour and cook over medium-high heat, stirring, for 2 to 3 minutes. Add the beef stock and sachet, bring to a simmer, and simmer for about 1 hour, or until the liquid is reduced to 2 1/2 quarts. Season to taste with salt, pepper, and a few drops of vinegar. Go easy on the seasonings, nothing should overpower the sweet onion flavor. Remove from the heat. (It’s best to let the soup sit for a day or so in the fridge to allow the flavors to deepen.)

Preheat the broiler. Cut twelve 3/8 inch thick slices from the baguette (reserve the remainder for another use) and place on a baking sheet. Brush the bread lightly on both sides with olive oil and sprinkle lightly with salt. Place under the broiler and toast the first side until golden brown, then turn and brown the second side. Set aside and leave the broiler on.

Place the tureens under the broiler until the cheese bubbles, browns, and forms a thick crust. Eat carefully, the soup and tureens will be very hot.