Preheat the oven to 350°F (175°C).

Melt 2 tablespoons of butter in a large skillet over medium heat. Add the sliced onions and cook, stirring occasionally, for 20-25 minutes until golden and caramelized. Remove half of the onions and set them aside for the sauce.

In a large bowl, combine the ground beef, eggs, breadcrumbs, Worcestershire sauce, thyme, salt, pepper, and the remaining half of the caramelized onions. Mix gently until just combined.

Shape the meat mixture into a loaf and place it in a baking dish or loaf pan. Bake for 45 minutes.

While the meatloaf bakes, return the reserved onions to the skillet. Add the remaining 1 tablespoon of butter and let it melt. Stir in the flour and cook for 1 minute, whisking constantly. Gradually whisk in the beef broth and simmer for 5-7 minutes, stirring occasionally, until the sauce thickens slightly.

Remove the meatloaf from the oven and top with the shredded Swiss cheese, followed by the slices of provolone. Return to the oven and broil for 3-5 minutes, or until the cheese is melted and golden.

Let the meatloaf rest for 5-10 minutes before slicing. Serve the meatloaf with the onion sauce spooned over the top. Enjoy!