Pat the chicken dry with paper towels and season with salt and black pepper.
Heat 1 tablespoon butter in a large skillet over medium heat. Place chicken thighs skin-side down and cook for 4 to 5 minutes until browned. Flip and cook for another minute. Remove and set aside.
Add drumsticks to the skillet and brown for about 2 minutes per side. Remove and set aside with the thighs.
Add remaining butter to the skillet. Stir in onion and garlic and sauté for about 1 minute until fragrant.
Reduce heat to low and stir in sweet Hungarian paprika and smoked paprika. Mix well to coat the onions.
Pour in chicken broth and stir. Return chicken pieces to the skillet skin-side up.
Cover and simmer over medium-low heat for 10 minutes.
Uncover and continue cooking for another 20 minutes until the chicken is fully cooked and tender. Remove chicken and keep warm.
In a small bowl, whisk together sour cream, flour, and water until smooth.
Slowly stir the sour cream mixture into the sauce while whisking constantly to avoid lumps. Cook for 2 to 3 minutes until creamy. Simmer longer for a thicker sauce if desired.
Return chicken to the skillet and spoon sauce over the top.
Garnish with fresh parsley and serve warm.