Salt and pepper the chicken pieces. Melt the butter in a large heavy skillet or pot. (Choose a pot with a tight-fitting lid available. This dish is brazed, so a lid will be needed.) Add as many chicken pieces as will fit in the pot without touching. Brown the chicken on both sides, 3-4 minutes per side, working in batches if needed. (If the chicken is crowded in the pot, it will start to steam, not brown. A good brown "sear" of the chicken is desirable here.) Transfer browned chicken pieces to a plate, and continue until all chicken is browned. 

Using the same pot, and without cleaning it, add onions and cook until they start to sweat and brown, 5-6 minutes. Scrape the bottom of the pot with your spatula while cooking the onions, to remove all the stuck chicken bits and brown stuff that appeared while you cooked the chicken. (This is flavor! Get as much as you can!) Add the peppers and cook until soft, continuing to stir and scrape as they cook. Add garlic and cook one minute more. Add tomato paste and stir to combine, cooking for an additional two minutes or so. Turn off the heat, and stir in the paprika. Take a moment to stir and combine well, so the paprika coats all parts of the dish. 

Return to medium-high heat, and add the chicken broth. Add the chicken back to the pot, along with any juices that may be on the plate. Bring to a boil, then reduce heat to low, cover, and simmer for 30-40 minutes, until chicken is fork-tender. Taste and adjust salt and pepper!

Put the sour cream in a small bowl, and temper it by adding small spoonfuls of hot paprikash sauce to it, a little at time. This will raise the temperature of the sour cream slowly, so it doesn't curdle when added to the hot sauce. Do this 5-6 times, until the sour cream is no longer cold. If desired, add 1 tsp of paprika to the sour cream. Add the tempered sour cream to the paprikash, stir, and simmer 8-10 minutes more. Be sure not to bring the sauce to a full boil at this point, so the sauce stays creamy. 

Serve immediately, with rice, buttered egg noodles, potatoes, or any other side dish. Add a dollop of sour cream to the top!