Heat broiler to high. Wash and dry all produce. Halve, peel, and very thinly slice onions. Pick thyme leaves from stems; mince leaves until you have 1 tsp (2 tsp for 4), reserving a few whole leaves for garnish. Trim ends from baguette; slice crosswise into 6 equal-size rounds (12 rounds for 4 servings). Halve lemon. In a small bowl, combine juice from whole lemon, a large drizzle of olive oil, and mustard to taste. Season with salt and pepper; set aside.

Heat a large pot over medium-high heat; add a large drizzle of olive oil and 1 TBSP butter. Add onions and 1/2 tsp salt (1 tsp for 4). Cook, stirring occasionally, until onions are slightly softened and browned, 8-10 minutes. Stir in 1/4 cup water, scraping up any browned bits from bottom of pan. Cook, without stirring, 8-10 minutes more. Add another 1/4 cup water, scraping up any browned bits from bottom of pan; cook, stirring occasionally, until deeply browned and caramelized, 8-10 minutes more. TIP: If onions start to burn, add a splash of water.

To pot with caramelized onions, add vinegar, minced thyme, 1 TBSP sugar (2 TBSP for 4 servings), and 1/4 cup water. Cook until deeply browned and jammy, 2-3 minutes. Add stock concentrates and 3 cups water (5 cups for 4). Bring to a simmer and cook, stirring occasionally, until flavors meld, 3-5 minutes. Taste and season with salt and pepper.

Meanwhile, halve, core, and thinly slice half the apple (whole apple for 4 servings) into half-moons. In a large bowl, toss apple slices and mixed greens with as much dressing as you like. Season with salt and pepper.

Place baguette slices on a baking sheet and top evenly with Gruyère. Broil on top rack until cheese is melted and bubbly, 2-3 minutes. TIP: Watch carefully to avoid burning.

Divide soup between bowls. Top with Gruyère toasts. Garnish with reserved thyme leaves as desired. Serve with salad on the side.