1. Heat a medium soup pot over medium-low heat. Add salted butter.
2. When butter melts, add yellow onions, Cook, stirring occasionally, for 20 to 30 minutes, or until a deep caramel brown.
3. Add beef broth, dry white wine, bay leaf, dried thyme, sea salt, and black pepper. Stir, cover, and shimmer for 20 minutes. Remove and discard bay leaf.
4. Preheat the broiler to high and place a rack on the highest shelf.
5. Place 4 oven proof crocks or metal bowls on a rimmed metal baking sheet.
6. Divide soup into the 4 crocks. Cover with Gruyere and Parmigiano-Reggiano.
<a href="" title="">