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.
I haven't made this yet, but my grandfather is from Hungary, and this is one of our favortie dishes. I just wanted to add that the real traditional way to make this, is an all day project. and the traditional way it is served with is homeade dumplings. that are scrapped throught a dumpling maker then boiled. YUM!! ill have to compare the 2 and see which is better.
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