To a large non-stick skillet over medium-low heat, melt ¼ cup of butter.
Once melted, add onions and saute for 25-30 minutes, stirring occasionally, until they are very tender and caramelized to a rich golden brown color.
While the onions are caramelizing, bring a large pot of salted water to a boil. Add pasta and cook until al dente (about 8-10 minutes). Reserve 1 cup of pasta water and drain the rest.
Once the onions are caramelized, carefully transfer them to the bowl of a food processor. Set aside.
To a microwave-safe bowl, add the remaining ½ cup butter. Heat until melted.
Pour the melted butter into the bowl of the food processor with the caramelized onions.
Add ½ cup of reserved pasta water to the food processor and blend until the mixture is well blended. Set aside while you prepare the chicken.
Season the chicken breasts evenly with paprika, 1 teaspoon salt, and pepper.
In the same skillet over medium heat, add the olive oil. Once hot, add the seasoned chicken breasts.
Cook the chicken for 5 minutes on one side. Then, flip the chicken over, reduce the heat to medium-low, and cook for an additional 5 minutes or until the chicken reaches an internal temperature of 165°F. Remove the chicken from the skillet and transfer it to a plate. Tent with aluminum foil to keep warm.
To the same skillet over medium heat, add the onion mixture, heavy cream, parmesan, and remaining ½ teaspoon salt. Cook until cheese is melted and the sauce is heated through.
Add the cooked pasta to the skillet and toss until the noodles are evenly coated in the creamy sauce. If the sauce appears too thick, add a bit more of the reserved pasta water to reach your desired consistency.
Slice the cooked chicken breasts into strips and arrange them on top of the pasta.
Serve hot, garnished with additional grated parmesan cheese and freshly chopped parsley. Salt and pepper to taste.