Step 1

Melt butter in a large pot or Dutch oven over medium heat. Add onion and stir to coat. Reduce heat to low; cover and cook 15 minutes.

Step 2

Meanwhile, make the toasted bread cubes (croutons): Preheat oven to 400°F.

Step 3

Line a baking sheet with parchment paper and spread bread cubes in a single layer. Bake until crisp and golden brown, 12 to 15 minutes. Remove from oven and set aside.

Step 4

Uncover onions and stir in salt and sugar. Raise heat to medium-low; cook 40 to 50 minutes, stirring often until onions have caramelized to a deep golden brown.

Step 5

Add flour; cook and stir 3 minutes to remove flour taste. Add thyme, wine, and mushroom broth to onion mixture and stir, scraping up any browned bits. Increase heat to medium-high and bring to simmer. Reduce heat and let simmer, stirring occasionally, 30 to 40 minutes to your desired taste and consistency. Remove from heat and stir in Cognac. Add salt and pepper to taste

Step 6

Preheat broiler.

Step 7

Ladle soup into 6 individual broiler-safe bowls. Top each bowl with 1/6 each of the toasted bread cubes and shredded cheese.  Arrange bowls on a baking sheet and place under broiler. Broil until cheese is melted and bubbly. Serve.