Preheat oven to 400°F (200°C) and prepare a 9×13 inch baking dish with cooking spray.
In a large pan over medium heat, melt butter. Add onions, cooking until soft, sweet, and golden (about 15 minutes). Mix in garlic, salt, pepper, and thyme, cooking for another minute.
Sprinkle flour over onions, cook for a couple of minutes, then add wine. Simmer until reduced slightly, then add both broths and simmer for 10 more minutes.
Layer half the onion mix in the dish, top with bread slices, and sprinkle half the Gruyère and Parmesan. Repeat layers.
Bake uncovered for 20-25 minutes, until cheese is bubbly and golden. Let sit before serving and garnish with parsley.
