Pour vegetable oil into a large Dutch oven or other heavy-bottomed pot over medium-high heat. Add chicken and brown well on each side, about 4–5 minutes per side (the skin should be crisp). Don’t overcrowd the pot; cook in batches if necessary.
Remove to a plate. Discard all but 1 tablespoon of fat from pot.
Reduce heat to medium-low; add onion and salt to pot and cook until just translucent, about 5 minutes.
Stir in garlic, tomatoes, peppers, flour, paprika, and pepper; cook, stirring often, about 5 minutes.
Return chicken and any juices to pot. Add stock and bring to a boil. Reduce heat to a simmer and cover. Cook 15 minutes; then turn chicken. Simmer until chicken is fully cooked, 10-12 minutes more.
In a medium-size bowl, whisk together sour cream and 1 cup sauce from the pot.
Remove pot from heat and stir sour cream mixture into sauce. Taste and add extra salt as needed. Garnish with chopped parsley and serve with rice or dumplings.