In a saucepan, combine the vinegar, sugar and bay leaf; season with pepper and bring to a boil over medium-high heat, stirring until the sugar is dissolved. Pour the mixture over the onion, cover and let stand for 20 minutes. Drain.
Rub the toasted bread with the garlic. Season the tuna with salt, pepper and the thyme. In a skillet, heat the EVOO, 2 turns of the pan, over medium-high heat. Add the tuna and cook until just about opaque, about 5 minutes. Flake the tuna into chunky pieces.
Preheat the broiler. Spread a light layer of mustard on each baguette slice, then top with tuna, onions, cornichons and cheese. Place on a baking sheet and broil until the cheese is melted.