Caramelize the onions: Set a 6-quart Dutch oven over medium heat. Add olive oil and butter. When melted and glossy, add the sliced onions and a pinch of salt. Cook low and slow, stirring every few minutes, until deeply caramelized and coppery-brown, 60–90 minutes. If onions look dry at any point, stir in 1–2 teaspoons water to prevent scorching.
Build extra fond and add garlic: Raise heat to medium-high for 2–3 minutes to develop browned bits on the pot bottom (fond). Stir in minced garlic and cook 30–60 seconds until fragrant (do not brown).
Deglaze without alcohol: Pour in the no-alcohol deglaze (beef stock + apple cider vinegar, or white grape juice + stock). It will hiss. Scrape up all the browned bits with a wooden spoon until the pot bottom is clean and glossy; reduce for about 1 minute.
Thicken lightly: Sprinkle flour over the onions and stir constantly for 1 minute to cook off raw flour taste. (Gluten-free option: skip flour here and thicken later with a cornstarch slurry—1 tbsp cornstarch whisked with 1 tbsp cold water.)
Simmer the broth: Add Worcestershire sauce, fish sauce, thyme sprigs, bay leaf, black pepper, and the beef stock. Bring to a lively simmer, then reduce to low and cook 25–40 minutes with the lid slightly ajar, stirring occasionally. Taste and adjust salt and pepper. If using cornstarch slurry, whisk it in now and simmer 1–2 minutes to thicken.
Toast the bread: While soup simmers, preheat oven to 400°F (200°C). Brush baguette slices with olive oil and bake 5–8 minutes until crisp and golden. While warm, rub tops with the cut side of the halved garlic clove.
Broil and finish: Switch oven to BROIL. Remove thyme sprigs and bay leaf from soup. Ladle hot soup into oven-safe bowls on a baking sheet. Float 1–2 toasts in each bowl. Top with a generous mix of shredded Gruyère and Comté (about 1/3–1/2 cup per bowl). Broil 3–5 minutes until cheese is melted, bubbly, and browned in spots.
Serve: Let bowls rest 2 minutes (they’re very hot). Garnish with chopped chives or thyme leaves if desired. Serve immediately and enjoy.