Cook the Onions: Heat the olive oil and butter in a large deep skillet over medium heat. Add the sliced onions, salt, and black pepper. Cook for 25 to 30 minutes, stirring every few minutes, until the onions become deeply golden and very soft. If they begin browning too quickly, lower the heat and add 1 tablespoon of water. This slow cooking process is crucial for developing the rich, sweet flavor characteristic of caramelized onions.

Add the Aromatics: Stir in the garlic and thyme. Cook for about 1 minute until fragrant, stirring constantly to prevent the garlic from browning. This step enhances the overall flavor profile, adding depth to the dish.

Build the Broth: Add the vegetable broth, Dijon mustard, balsamic vinegar, and bay leaf. Stir well, scraping up any browned bits from the bottom of the skillet. These bits add a layer of flavor to the broth, making it more savory and complex.

Add the Beans: Stir in the drained cannellini beans. Bring the mixture to a gentle simmer over medium heat. The beans will soak up the flavors from the broth, enhancing their creamy texture and taste.

Simmer Gently: Cover partially and cook for 10 to 12 minutes, stirring occasionally, until the beans are heated through and have absorbed some of the broth. The sauce should remain slightly brothy rather than dry. This ensures that the beans stay moist and flavorful.

Finish with Cheese: Remove the bay leaf: Reduce the heat to low and sprinkle in the Gruyère a handful at a time, stirring gently until melted and incorporated into the broth. This step adds a creamy richness to the dish, reminiscent of traditional French onion soup.

Rest the Beans: Remove the skillet from the heat and let the beans rest for 5 minutes. The broth will thicken slightly as the cheese settles. Allowing the dish to rest helps the flavors meld together.

Serve: Sprinkle with chopped parsley and additional thyme, if desired. Serve warm with toasted baguette slices for dipping. This adds a delightful crunch and enhances the overall dining experience.