Heat the butter and oil in a wide heavy pot over medium heat. Add the sliced onions and stir to coat. Cook uncovered for 45–60 minutes or longer, stirring regularly and more frequently as they brown, until very soft and deep golden brown. Lower the heat if they darken unevenly. Add small splashes of water to release browned deposits as needed; leave any black burned bits behind.

Stir in the garlic for 30 seconds. Add the wine and scrape up the brown deposits. Simmer for 2–3 minutes, then add stock, thyme, bay leaf, Worcestershire and pepper.

Bring to a gentle simmer and cook partly covered for 20–25 minutes. Remove the thyme stems and bay leaf. Taste, then add the measured salt a little at a time only as needed. Add a splash of water if the broth has reduced more than you prefer.

While the soup simmers, heat the oven to 400°F (200°C). Toast the baguette slices on a metal baking sheet for 6–10 minutes, turning once, until dry and lightly golden on both sides.

Set four broiler-safe crocks on the rimmed metal baking sheet and divide the hot soup between them, leaving headroom. Top each with one toast and one-quarter of the grated cheese. Broil about 6 inches from the heat for 1–3 minutes, watching continuously, until the cheese melts and browns in spots. Use only dishes rated by their manufacturer for broiler heat. If unavailable, broil cheese on the toasts separately on the sheet and set them on the hot soup.

Let the bubbling subside briefly, then serve the crocks on heatproof plates, warning that bowls and soup are very hot. Store extra broth without toast in shallow containers, refrigerate within 2 hours and use within 3–4 days. Reheat broth to 165°F (74°C) and bring it to a boil before adding freshly prepared cheese toasts.