Brown the chicken. Season the chicken with a generous pinch of salt, pepper, and dried parsley. Meanwhile, add the butter and olive oil to a large Dutch oven or skillet with high sides over medium-high heat. Add the chicken thighs, skin-side down, and brown for approximately 4-5 minutes before flipping and browning the other side for an additional 4-5 minutes. Carefully remove chicken from the pot to a clean plate and set aside.
Cook the onions. Reduce heat to medium and add the onions. Scrape up any leftover brown bits from the chicken that may be stuck to the bottom of the pot. Cook the onions, stirring occasionally, for 6-8 minutes. Add the garlic and cook for 1 minute. Reduce heat to low and add the salt, pepper, cayenne (optional) and Hungarian Sweet Paprika. Cook for 1-2 minutes, stirring constantly to prevent the Paprika from burning.
Return the chicken back to the pot. Add the chicken broth to the onions and bring to a simmer. Add the chicken back to the pot and cover with a tight-fitting lid. Allow chicken to slowly simmer for approximately 30-35 minutes, or until fully cooked.
Boil egg noodles. As the chicken simmers, cook the egg noodles according to package instructions. Drain, rinse with cool water, return back to pot, and toss with approximately 1-2 tablespoons of butter to help prevent them from sticking.
Prepare the sour cream mixture. As the chicken AND the egg noodles cook, whisk together the sour cream and all-purpose flour. Set aside.
Add the sour cream mixture. As soon as the chicken is fully cooked, carefully remove to a clean plate and cover with foil to keep warm. Add the sour cream and flour mixture to the onions, mixing well to combine.
Serve. Return the chicken back to the pot to keep warm until ready to serve. Serve garnished with fresh chopped parsley and additional sour cream, if desired.