Before you start cooking, peel the onion and chop it roughly. Salt chicken pieces from all sides.
In a wide pan with a thicker bottom, melt lard over higher heat. Place the chicken to the lard and fry each side for about 5 minutes. Remove the chicken and set it aside.
Reduce heat to medium. Add chopped onions to the same pan and fry until translucent. Use a flat-edged spatula and scrape the burned-on rests of the chicken from the pan's bottom. These are very tasty and deserve to be a part of chicken paprikash.
Add sweet Hungarian paprika and fry for 30 sec until stirring.
Pour with chicken broth, return the fried chicken pieces to the pan. Salt a bit, throw allspice berries into the liquid. Bring to a boil, then reduce the heat to a minimum. Cover with a lid and allow paprikash to simmer for 40 minutes or until the chicken meat is soft and tender.
Remove the cooked chicken, set it aside, keep the meat warm.
Make a roux: In a non-sticking pan, melt butter over medium heat until it starts to bubbling. Sprinkle in the all-purpose flour, fry for 1-2 minutes while stirring. Add the roux into the paprikash in small batches, whisk properly to avoid lumps.
Cover with a lid and let the sauce simmer for 15-20 minutes.
Remove from the stove, add sour cream, do not cook anymore. Stir well.
Strain the paprikash over a sieve. Discard rests got stuck in the sieve (onions, allspice berries).
Season the paprikash with salt to your liking. Optionally, add ½ teaspoon sugar.
Put chicken pieces back in a pan, let them warm up, and serve.