Preheat the oven to 180°C (350°F).
Season the chicken with the salt and black pepper.
Heat the goose fat in a Dutch oven over medium-high heat. Working in batches, add the chicken skin-side down and cook for 4–5 minutes, until golden brown. Flip and cook for another 2 minutes. Remove and set aside.
Reduce the heat to medium. Add the onion and cook for 4–5 minutes, until softened and golden brown. Add a little of the chicken resting juices if needed to deglaze the pan.
Add the green bell pepper and cook for 2–3 minutes, until softened.
Add the Hungarian paprika and cook for 30–60 seconds, stirring constantly.
Pour in the chicken stock and bring to a boil.
Return the chicken and any resting juices to the Dutch oven. Cover and bake for 45 minutes, until the chicken is fully cooked and tender.
Remove from the oven and place the Dutch oven over medium-high heat. Simmer uncovered until the sauce has reduced to your desired consistency.
Add a few spoonfuls of the hot sauce to the sour cream in a small bowl and mix until smooth.
Reduce the heat to low. Stir the sour cream mixture into the sauce until fully combined.
Serve immediately.