Cook onions, along with thyme, bay leaves, and salt in butter in a heavy stockpot over medium heat, uncovered, stirring frequently, until onions are very soft and deep golden brown, about 30 minutes, lowering heat if browning too quickly.
You don’t want them to burn.
Sprinkle flour over the onions, and cook, stirring, about 1 minute.
Pour in wine and cook, stirring, another minute.
Stir in broth, water, garlic, and pepper and simmer uncovered, stirring occasionally, about 20 to 30 minutes, or until lightly thickened.
Check and adjust seasonings.
Preheat broiler. Remove and discard bay leaves; place bread slices at the bottom of heat-safe/broiler-safe crocks; then spoon generous amounts of broth and onions over bread.
Top with Brie, then cover the top with Parmesan.
Broil 4 to 5 inches from heat until cheese is melted and bubbly, 1 to 2 minutes.
For each crock:
1 slice, buttered and toasted French or Italian Bread slice, then each cut into quarters
1 thick slice of Brie Cheese (to your liking)
2 tablespoons freshly shaved Parmesan cheese
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