Preheat the oven to 375 degrees and lightly grease a loaf pan. In a skillet over medium heat, cook the mushrooms and onion until the liquid evaporates and the vegetables soften. Add the garlic and cook for one more minute, then set the mixture aside to cool slightly.
In a mixing bowl, combine the ground beef, cooled mushroom mixture, egg, half the Swiss cheese, 2 tablespoons thyme, and a pinch of salt and pepper. Mix gently until just combined.
Press the meat mixture into the prepared loaf pan. Bake for 45 to 50 minutes until the internal temperature reaches 160 degrees. Sprinkle the remaining cheese over the top during the last 10 minutes of baking.
While the meatloaf rests, make the jus. In the same skillet, add the beef broth and remaining tablespoon of thyme. Bring to a simmer and cook until reduced by about one third. Stir in the butter until melted and season with salt and pepper to taste.
Slice the meatloaf and serve with the thyme jus spooned over each portion.