Season the chicken with 3/4 teaspoon of the salt and the black pepper.
Heat the oil in a Dutch oven over medium-high heat. Working in batches, add the chicken, skin-side down. Cook, without turning, until golden brown, 4 to 5 minutes. Turn and cook for 3 minutes more. Transfer the chicken to a plate.
Spoon off and discard all but 1 tablespoon of the fat. Add the onion and bell pepper and cook for 2 minutes. Add the broth and cook, stirring, for 1 minute. Add the tomatoes and their juices, the paprika, and the remaining salt. Bring to a simmer.
Return the chicken to pot. Transfer to oven. Bake until the chicken is cooked through, about 30 minutes.
Meanwhile, in a small bowl, combine the cucumber and vinegar (if desired).
Divide the chicken among plates and serve with a dollop of the sour cream and the cucumbers (if serving).
Tip: This hearty Hungarian dish is traditionally served with flat egg noodles. You can also spoon it over white rice or instant polenta.