Pat the chicken thighs completely dry with paper towels. Season generously on all sides with kosher salt and black pepper.

Heat the vegetable oil and butter in a large Dutch oven or heavy-bottomed pot over medium-high heat. Once the butter is melted and sizzling, carefully place the chicken thighs skin-side down. Sear for 5-7 minutes without moving, until the skin is golden brown and crispy. Flip and sear the other side for another 3-4 minutes. You may need to do this in batches to avoid overcrowding the pot. Transfer the browned chicken to a plate and set aside.

Reduce the heat to medium. Add the finely chopped onions to the pot, scraping up any browned bits from the bottom. Cook, stirring occasionally, for 8-10 minutes until the onions are very soft and translucent.

Stir in the minced garlic and tomato paste. Cook for 1 minute more until fragrant.

CRITICAL STEP: Remove the pot from the heat completely. This prevents the paprika from burning and becoming bitter. Add the sweet and hot (if using) paprika and stir constantly for 30 seconds until the onions are fully coated and fragrant.

Immediately pour in the chicken broth, whisking to combine everything smoothly. Return the pot to the stove and bring the mixture to a simmer.

Return the browned chicken thighs (and any accumulated juices from the plate) to the pot, nestling them into the sauce. Reduce the heat to low, cover the pot, and let it simmer gently for 30-35 minutes, or until the chicken is tender and cooked through (internal temperature reaches 165°F or 74°C).

While the chicken simmers, prepare the sour cream mixture. In a medium bowl, whisk together the room temperature sour cream and the all-purpose flour until no lumps remain.

Once the chicken is cooked, temper the sour cream. Carefully ladle about 1 cup of the hot sauce from the pot into the sour cream mixture, whisking constantly until smooth. This warms the sour cream gently to prevent it from curdling.

Pour the tempered sour cream mixture back into the pot with the chicken. Stir gently to combine. Let the sauce heat through for 2-3 minutes until it thickens slightly. Do not allow it to boil. Taste and adjust seasoning with more salt and pepper if needed.

Serve the chicken paprikash hot, spooning the rich sauce over the chicken. It's traditionally served with nokedli (Hungarian dumplings), wide egg noodles, or mashed potatoes. Garnish with fresh chopped parsley before serving.