Over medium heat, add olive oil and butter in a large pot or Dutch oven. Once hot, add the sliced onions. Stir occasionally, letting the onions caramelize slowly for about 35-40 minutes.
Add minced garlic and thyme to caramelized onions, and cook for 1-2 minutes until garlic is aromatic. Sprinkle brown sugar over the onions, stir well, and cook for 2 minutes.
Pour in dry the white wine to deglaze the skillet, scraping any brown bits. Add vegetable broth and simmer and let the sauce reduce for 10 minutes.
Meanwhile, cook the pasta in salted boiling water until al dente.
Add the cream cheese to the sauce, stirring until the sauce is smooth. Then stir in the shredded Swiss cheese.
Once the cheese has melted, add the drained pasta and toss to combine. If desired, season with salt and pepper.