Melt butter in a large, heavy-bottom pot over medium-low heat. Add onions, and cook, stirring occasionally, for 60 to 90 minutes until softened and caramelized with a golden-brown hue.
Add Calvados, and stir to combine, scraping up any bits stuck to the pan. Let alcohol burn off, 2 to 3 minutes. Add stocks, bay leaves, and thyme, and stir to combine. Bring to a simmer, and cook 30 minutes, then season with salt and pepper. Discard bay leaves and thyme.
Place rack in the upper ⅓ of oven and heat broiler. Ladle soup into 4 oven-safe crocks and place on a baking sheet. Top each with 2 baguette slices and sprinkle with ¼ cup cheese. Broil until cheese is melted and bubbly, about 1 to 3 minutes, depending on the strength of your broiler. Serve immediately.