In an oven & stovetop safe deep large skillet, add the butter, onions, salt, sugar, and pepper over medium-high heat.
Sauté for about 15 minutes until the onions start to turn golden brown. Deglaze the pan with about ⅓ of the wine.
Sauté for another 30 minutes, deglazing the pan twice more with the remaining wine (every 15 minutes). After 45 minutes, the onions should have reduced significantly in volume and be a deep brown color. See photos above.
Reduce to medium-low heat. Add the garlic and thyme. Sauté for about 1-2 minutes. Preheat the oven to 375 degrees.
Stir in 2 cups of broth, milk, worcestershire, and the pasta. Increase to medium heat and bring to a light boil. Cook and stir occasionally for about 10 minutes.
Stir in the remaining cup of broth.
Continue cooking for about 5-10 minutes or until the pasta is almost cooked through. If the pasta seems dry at any point, add a broth splash. Taste and add salt if needed.
Remove the pasta from the heat and stir in about 2 cups of the cheese.
Sprinkle the remaining cheese and crispy onions on top.
Bake for 10-15 minutes. Let stand for 5 minutes before serving.