Heat 3 Tbsp. extra-virgin olive oil in a large high-sided ovenproof skillet over medium-high heat. Add 4 large yellow onions, a pinch of kosher salt, and a pinch of freshly ground black pepper, cooking until onions are deep mahogany color and jammy, about 30-35 minutes.

Add 6 garlic cloves and 4 tsp. chopped thyme, cooking until fragrant, about 1 minute. Add ¾ cup dry white wine and reduce by half, about 3 minutes. Add 5½ cups water and bring to a simmer.

Add 1 lb. lumache pasta and cook, stirring to prevent sticking, until liquid is absorbed and pasta is al dente, about 10-14 minutes.

Remove from heat and stir in 1 oz. Parmesan, 5 Tbsp. unsalted butter, 1 Tbsp. Dijon mustard, 2 tsp. sugar, 2 tsp. Worcestershire sauce, remaining 2 tsp. kosher salt, and remaining 1 tsp. black pepper until cheese is melted.

Place a rack in upper third of oven; heat broiler. Scatter 8 oz. Gruyère over pasta and broil until melted and golden brown, 2-5 minutes.

Top with thinly sliced chives if using before serving.