Heat butter or oil in a heavy-bottom skillet over medium-high heat. Sear chicken skin-side down for 4-5 minutes until golden brown, then flip and cook for 3 more minutes. Transfer chicken to a plate and leave 2 tablespoons of fat in the pan.
2 lbs bone-in skin-on chicken thighs or drumsticks, 2 tablespoons butter or neutral oil
Add diced onion to the skillet and sauté for 5-6 minutes over medium heat until soft and translucent. Add minced garlic and cook for 30 seconds until fragrant. Remove pan from heat.
1 large onion, 2 cloves garlic
Stir in sweet Hungarian paprika off direct heat for 30 seconds to coat the onions completely. Return pan to heat and add flour. Cook the flour roux for 2-3 minutes, stirring constantly until light golden and no raw flour taste remains.
2 tablespoons sweet Hungarian paprika, 2 tablespoons all-purpose flour
Deglaze the pan with chicken broth, scraping browned bits from the bottom. Return chicken to the pan, skin-side up, and bring to a gentle simmer. Cover and simmer for 35-40 minutes until chicken reaches an internal temperature of 165°F.
1.5 cups chicken broth, 2 lbs bone-in skin-on chicken thighs or drumsticks
Temper the sour cream by slowly whisking in ¼ cup of the hot sauce from the pan. Stir the tempered sour cream into the remaining sauce off heat. Season with salt and black pepper. Let the dish rest for 10 minutes before serving.
0.75 cup sour cream, to taste salt and black pepper