Season and Sear the Chicken: Pat the chicken pieces dry and season them generously with salt and freshly ground black pepper. In a large Dutch oven or heavy-bottomed skillet, heat the vegetable oil over medium-high heat. Add the chicken, skin side down, and cook until the skin is golden brown, about 5-7 minutes. Flip and brown the other side for an additional 5-7 minutes. Remove the chicken from the pot and set aside.
Sauté Onions and Garlic: In the same pot, reduce the heat to medium and add the unsalted butter. Once melted, add the thinly sliced onions and cook, stirring occasionally, until softened and translucent, approximately 6-8 minutes. Add the minced garlic and cook for another minute until fragrant.
Incorporate Paprika and Flour: Sprinkle the Hungarian sweet paprika, all-purpose flour, and cayenne pepper (if using) over the onion mixture. Stir continuously for about 2 minutes to toast the spices and eliminate the raw taste of the flour.
Add Broth and Simmer: Slowly pour in the low-sodium chicken broth, stirring constantly to prevent lumps. Bring the mixture to a simmer, ensuring it is well combined. Return the browned chicken pieces to the pot, nestling them into the sauce. Cover the pot, reduce the heat to low, and let it simmer gently for 35-40 minutes, or until the chicken is cooked through and tender.
Finish with Sour Cream: Once the chicken is tender, remove the pot from the heat. Carefully transfer the chicken pieces to a plate. Whisk the sour cream into the sauce until smooth and creamy. Return the chicken to the pot, ensuring each piece is coated with the sauce.
Serve: Garnish the chicken paprikash with chopped fresh parsley. Serve hot over cooked egg noodles or traditional Hungarian dumplings, allowing the sauce to envelop the noodles.
