Heat the vegetable oil in a large skillet or Dutch oven over medium-high heat.
Season the chicken thighs with salt and black pepper. Once the oil is hot, add the chicken thighs to the skillet, skin side down. Brown them for about 5-7 minutes until the skin is crispy, then flip and brown the other side for another 5-7 minutes. Remove the chicken and set aside.
In the same skillet, add the chopped onion and sauté for about 5 minutes until softened. Add the minced garlic and sliced bell pepper, and cook for an additional 2-3 minutes.
Stir in the sweet Hungarian paprika, ensuring the onions and peppers are well coated.
Pour in the chicken broth, scraping the bottom of the skillet to lift any browned bits. Return the browned chicken thighs to the skillet, cover, and let simmer for 25 minutes.
After 25 minutes, remove the chicken and reduce the heat to low. Stir in the sour cream until the sauce is creamy. Adjust seasoning if necessary.
Return the chicken to the sauce and heat through for another 5 minutes, allowing the flavors to meld.
Serve hot, garnished with fresh parsley, over dumplings or noodles, as preferred.