Heat vegetable oil in a large skillet over medium heat. Add the chopped onion and cook until softened and translucent, about 5 minutes.
Add minced garlic and cook for 1 minute until fragrant.
Stir in sweet Hungarian paprika, smoked paprika (if using), salt, and black pepper. Cook spices for 1 minute, stirring constantly to prevent burning.
Add chicken thighs to the skillet, browning them slightly on both sides, about 3-4 minutes per side.
Pour in chicken broth, bring to a simmer, then cover and let cook for 25 minutes until chicken is cooked through and tender.
In a small bowl, combine sour cream and flour until smooth. Temper this mixture by adding a few spoonfuls of hot cooking liquid from the skillet, stirring constantly.
Slowly whisk the sour cream mixture back into the skillet and cook uncovered for an additional 5 minutes, stirring frequently, until the sauce thickens.
Garnish with freshly chopped parsley and serve hot over egg noodles, rice, or mashed potatoes.