**Caramelize Onions:** Heat olive oil and butter in a large pot over medium heat. Add the sliced onions and cook, stirring occasionally, for 15–20 minutes until golden and caramelized. Sprinkle with sugar halfway through to enhance caramelization.
**Add Garlic and Seasonings:** Stir in the minced garlic, thyme, salt, and pepper. Cook for another 1–2 minutes until fragrant.
**Cook the Pasta:** Add the uncooked pasta to the pot, followed by the broth and water. Bring to a boil, then reduce the heat to medium-low. Cover and simmer for 10–12 minutes, stirring occasionally, until the pasta is tender and has absorbed most of the liquid.
**Add Cream and Cheese:** Stir in the heavy cream and 3/4 cup of the shredded cheese until melted and creamy. Adjust seasoning with additional salt and pepper if needed.
**Serve:** Remove from heat, sprinkle the remaining cheese over the top, and cover for 2–3 minutes to let it melt. Garnish with fresh parsley if desired and serve immediately.