Warm the lard in a large Dutch oven or heavy pot, then brown the chicken pieces well on all sides and move them to a plate. The browned bits left behind should look deep golden, because that fond builds the flavor of the finished sauce.
Add the onions to the same pot and cook until soft and golden brown, then stir in the garlic, tomatoes, and the Hungarian bell pepper if using for 2 to 3 minutes. The vegetables should look softened and glossy, with the onions fully golden rather than pale.
Take the pot off the heat and stir in the paprika, salt, and black pepper. You should smell a sweet, earthy fragrance right away, and removing the pot from the heat helps keep the paprika from turning bitter.
Return the chicken to the pot, pour in the chicken broth so the pieces are mostly covered, and bring everything to a boil. Once the liquid bubbles, cover the pot, lower the heat to medium-low, and keep it at a gentle simmer rather than a hard boil.
Cook for 40 minutes, then lift the chicken out to a plate again. The chicken should be tender and the broth should look darker, richer, and lightly reduced.
In a small bowl, mix the flour with the sour cream and heavy cream until completely smooth, then whisk this mixture into the sauce. The mixture should look lump-free before it goes in, which helps the final sauce stay silky.
Bring the sauce to a gentle simmer for a couple of minutes, whisking as needed, then season with more salt and pepper to taste. When it is ready, the sauce should coat the back of a spoon instead of looking watery.
Return the chicken to the pot and simmer briefly until heated through. The finished dish should look richly red-orange and creamy, with tender chicken tucked into the sauce.