Preheat oven to 425 degrees F (220 degrees C). Butter a baking sheet.

Cut a hole in the top of each bread round, leaving the sides and bottoms untouched, to make the opening of the bread bowl. Pull apart the cut-out section.

Place 1/2 cup butter and 2 tablespoons crushed garlic in a microwave-safe bowl. Heat until butter is melted, 2 to 4 minutes. Brush the insides of the bread bowls and the cut-out pieces with butter; place on the prepared baking sheet.

Bake in the preheated oven for 3 to 5 minutes. Leave oven on.

Melt the remaining butter in a large saucepan over medium heat. Add sweet onion. Cook and stir until onion has softened and turned translucent, about 5 minutes. Reduce heat to low and continue cooking and stirring until onion is very tender and dark brown, about 20 minutes more.

Stir the remaining garlic, beef broth, chicken broth, wine, and Worcestershire sauce into the onions. Bring to a boil. Reduce heat to low; cook until flavors intensify, 5 to 10 minutes. Spoon soup into each bread bowl. Cover soup with Gruyere cheese.

Bake in the preheated oven until cheese is bubbling and melted along the sides of the bread bowl, about 5 minutes.