Step 1

Toss onion and 3 Tbsp. oil in a large heavy pot to coat; season with salt. Cook over medium heat, stirring and scraping bottom of pot frequently, until onion softens, about 10 minutes. Reduce heat to low and add garlic. Cook, stirring and scraping pot’s surface occasionally, until onions are the color of browned butter (don’t worry if they stick in places; a few drops of water and a wooden spoon will release any sticky bits), 20–30 minutes longer. Add wine and cook, stirring and scraping up any browned bits, until wine is evaporated, about 3 minutes. Add 6 cups water and bring to a simmer. Season with salt and continue to simmer until flavors meld and soup tastes rich, 10–15 minutes.

Step 2

Meanwhile, preheat oven to 450°. Place bread on a rimmed baking sheet and drizzle with oil. Toast until lightly charred around the edges, about 10 minutes. Top with cheese and continue to toast until cheese is melted, about 5 minutes.

Step 3

Divide soup among bowls. Place cheesy toast on top. Sprinkle with chives and season with pepper.