Prep the onions: Peel and thinly slice the onions from root to tip. Keep slices even so they cook uniformly.
Start caramelizing: In a large skillet or Dutch oven, heat the butter and olive oil over medium heat.
Add the onions and salt, and cook, stirring every few minutes, until they soften and start to turn golden, about 10–12 minutes.
Deepen the color: Lower the heat slightly if the onions brown too quickly. Add sugar if using. Continue cooking, stirring occasionally and scraping the pan, until the onions are deeply caramelized and jammy, 25–35 minutes total.
Add aromatics: Stir in the garlic and thyme.
Cook for 30–60 seconds until fragrant.
Deglaze: Pour in the white wine (if using). Scrape up browned bits from the bottom of the pan. Let the wine reduce by half, about 1–2 minutes.
Add broth: Stir in the broth and Worcestershire sauce.
Bring to a gentle simmer.
Cook the pasta: Add the pasta directly to the skillet. Simmer, stirring often, until the pasta is al dente and the liquid has mostly absorbed, 10–12 minutes. Add more broth or water if it gets too dry before the pasta is done.
Make it creamy: Reduce heat to low.
Stir in the heavy cream and let it warm through for 1–2 minutes.
Add cheese: Sprinkle in Gruyère and Parmesan. Stir until melted and silky. Taste and adjust with salt and pepper.
Serve: Top with a little extra Gruyère, a crack of pepper, and chopped parsley.
Serve hot and enjoy the cozy, soup-like sauce clinging to every noodle.