Heat butter in a large, heavy pot over medium-high heat; cook and stir onions until they become translucent, about 10 minutes. Sprinkle onions with sugar; reduce heat to medium. Cook, stirring constantly, until onions are soft and browned, at least 30 minutes. Stir in garlic and cook until fragrant, about 1 minute.
Stir sherry into onion mixture and scrape bottom of pot to dissolve small bits of browned food from the pot. Transfer onions into a slow cooker and pour in beef broth. Season to taste with sea salt; stir in thyme and bay leaf. Cover cooker, set on High, and cook 4 to 6 hours. If desired, set on Low and cook 8 to 10 hours.
About 10 minutes before serving, set oven rack about 8 inches from the heat source and preheat the oven's broiler. Arrange bread slices on a baking sheet.
Broil bread slices until toasted, 1 to 2 minutes per side.
Combine Gruyere, Emmental, Parmesan, and mozzarella cheeses in a bowl, tossing lightly. Fill oven-safe soup crocks 3/4 full of onion soup and float a bread slice in each bowl. Top with about 2 tablespoons of cheese mixture per serving.
Place filled bowls onto a baking sheet and broil until cheese topping is lightly browned and bubbling, about 2 minutes.