Begin by slicing an onion in half lengthwise, and cutting it into ¼” thick slices.
With a large pot over high heat, add butter and allow to melt.
Add sliced onion, minced garlic, thyme, and bay leaves and sauté until onions are translucent and soften, about 5 minutes. Season with a few pinches of salt.
Reduce heat to medium-high and continue to cook the onion until soft and caramelized, stirring frequently.
As the onion gets closer to being caramelized, the bottom of the pan may start to burn, add a little bit of the beef broth to deglaze it as the onion continues to cook.
When the onions are a deep golden caramel color, about 25 minutes, add the rest of the beef broth to the pot.
Bring to a boil and simmer for another 10 minutes, season with salt and pepper to taste.
Shred or grate cheese, and slice bread into ¼” - ½” round slices that will fit inside an oven-safe bowl.
Remove thyme and bay leaves from the soup, and divide into oven-safe serving bowls.
When ready to eat, place a slice of bread on top of your soup and top generously with grated Fontina cheese.
Broil for 4 minutes until cheese is melted and golden.
Remove from oven and serve immediately. Enjoy!