Thinly slice the onions and mushrooms. Grate the cheese and slice the croissants in half horizontally. Preheat your oven broiler to high and set an oven-safe soup pot (or Dutch oven) on medium heat.

Melt 3 tbsp butter with 1 tbsp olive oil in the pot. Add the sliced onions and a pinch of salt. Cook on medium-low, stirring every few minutes. After 10 minutes add the sugar to aid caramelization. Total time about 20–30 minutes.

Push the onions to the side, add the remaining 1 tbsp butter, then the mushrooms. Sauté until they release their moisture and begin to brown, about 5–7 minutes. Stir in the minced garlic and cook for 30–60 seconds until fragrant.

Pour in the white wine and scrape any browned bits off the pot bottom. Let the wine reduce by half (1-2 minutes). Add the beef broth, extra cup of stock (if using), bay leaf, thyme sprigs, Worcestershire sauce (if using), and a splash of balsamic vinegar. Bring to a simmer and let the soup gently bubble for 15–20 minutes. Taste and season with salt and pepper.

While the soup simmers, split the croissants and place the halves cut-side-up on a baking sheet. Pile each half with a generous amount of grated cheese. Slide the sheet under the broiler until the cheese bubbles and turns golden brown, about 2–4 minutes.

Remove the thyme sprigs and bay leaf. Ladle hot soup into oven-safe bowls and float the cheesy croissant half on top or set on the side for dipping.