Heat 3 Tbsp. extra-virgin olive oil in a large (3½-qt. capacity or more) high-sided ovenproof skillet, rondeau, or other short-sided pot over medium-high. Add 4 large onions, thinly sliced, a pinch of kosher salt, and a pinch of freshly ground pepper and cook, stirring occasionally and adding 1 Tbsp. water and scraping bottom of pan if starting to burn, until onions are a deep mahogany color and jammy, 30–35 minutes. Add 6 garlic cloves, finely chopped, and 4 tsp. chopped thyme and cook, stirring often, until fragrant, about 1 minute. Add ¾ cup dry white wine and cook, stirring occasionally, until reduced by about half, about 3 minutes. Add 5½ cups water and bring to a simmer. Add 1 lb. lumache (snail shells) or other medium shell pasta and cook, stirring often to prevent pasta from sticking to bottom of pan, until almost all of the liquid has been absorbed, a thick sauce has formed, and pasta is al dente, 10–14 minutes.

Remove pot from heat and add 1 oz. Parmesan, finely grated (about ½ cup), 5 Tbsp. unsalted butter, 1 Tbsp. Dijon mustard, 2 tsp. sugar, 2 tsp. Worcestershire sauce, remaining 2 tsp. Diamond Crystal or 1¼ tsp. Morton kosher salt, and remaining 1 tsp. freshly ground pepper and stir until cheese is melted.

Place a rack in upper third of oven; heat broiler. Scatter 8 oz. Gruyère, coarsely grated (about 2 cups), over pasta and broil until melted and golden brown in spots, 2–5 minutes depending on your broiler.

Top with thinly sliced chives if using just before serving.