In a large skillet pan or cast iron braising dish (3.5 quart in size), slowly melt your butter on medium heat. Without letting the butter brown, add in the sliced onion. Start the onion caramelization process by cooking the onions for 15 minutes while stirring every couple minutes. This step is mostly to cook the water out of the onions.
When most of the water has evaporated, sprinkle in the sugar over the onions. Turn the heat down to medium-low heat. Keep stirring every 2-3 minutes for even cooking. It should take another 25-30 minutes to complete the caramelization process. Once the onion have a nice dark brown color, remove from the pan. If they get stuck to the pan, simply pour a tablespoon of the broth over the onions to deglaze and release them.
Keep the same pan on the stove and turn the heat up to medium-high. Drizzle with a tablespoon of olive oil and place the cubes of chicken in the pan. Also add in the minced garlic with the chicken with the teaspoon of salt and the teaspoon of thyme. Cook the chicken pieces through and keep them in the pan.
Deglaze the pan with the beef broth. Run your stirring utensil on the bottom of the pan to release any stuck on bits. Add in the caramelized onions and the uncooked pasta.
Bring the broth boil and turn the heat down to a simmer. Continue cooking until the pasta is al dente and has absorbed most of the liquids. Take the pan off of the heat.
Break apart the cream cheese in tablespoon pieces and stir in the pasta dish to melt and incorporate with the sauce. Do the same with the grated cheese.
Serve with the optional chopped fresh parsley and grated parmesan cheese.