In a large stainless steel saucepan, melt butter over medium-high heat until foaming. Add onions and cook, stirring occasionally, until softened, about 8 minutes
Lower heat to medium-low and cook, stirring frequently, until onions are very sweet and a rich golden-brown color, 1 to 2 hours. If browned onion juices on the bottom of the pot threaten to burn, add 1 tablespoon water, scrape up browned bits, and continue cooking
Season with salt and pepper. Add sherry and bring to a simmer, scraping up any browned bits. Cook about 3 minutes.
Add stock, thyme, and bay leaf; raise heat to medium-high; and bring to a simmer. Lower heat and simmer for 20 minutes. Add fish sauce and cider vinegar. Season with salt + pepper. Discard thyme and bay leaf
Preheat the broiler and adjust the rack to the top. Butter toast and rub with garlic until fragrant. Spoon a small amount of broth into the bottoms of oven-safe bowls
Then top with half the toast, and sprinkle cheese over. Spoon more soup, nearly filling the bowl. Set remaining toasts in bowls, and top with remaining cheese. Broil until bubbly & brown
Garnish with chives