Preheat the oven to 375°F. Line a rimmed baking sheet with parchment paper.
Combine the cubed bread, olive oil, salt, and black pepper in a large mixing bowl. Gently toss until well combined. Spread the bread on the prepared baking sheet and bake for 12-14 minutes or until golden brown and crispy.
While the croutons bake, start the soup. Melt the butter in a large pot over medium heat. Add the onions, salt, and sugar, and cook for 20-25 minutes, stirring occasionally, until the onions are golden brown and caramelized.
Stir in the minced garlic, dried thyme, and tomato paste. Sauté for 1-2 minutes or until combined and fragrant.
Add the cornstarch and sauté for 1 more minute, until combined and toasty.
Stir in the chicken broth, vinegar, soy sauce, and chicken bouillon, scraping the bottom of the pan well to release any of the browned bits. Bring to a simmer and cook uncovered for 20 minutes.
Season the soup to taste with salt and cracked black pepper, and serve it hot, garnished with croutons and the shredded cheeses.