Preheat 2 tablespoons of lard to a large skillet and place on a stovetop set to medium-high heat. Add onions and turn the heat down to medium heat. Sauté until they begin to turn golden brown on the edges.
Move onions the the outer edges of the skillet.
Add 1 more tablespoon of lard to center of the skillet, and place chicken pieces down evenly in the center of the skillet. Cook on each side for about 1 or 2 minutes, until parts are slightly golden brown. Remove pan from heat.
Add Hungarian sweet paprika and optional Hungarian hot paprika (or optional cayenne pepper) to the pan with the chicken and onions and give it a quick stir.
Add onion and chicken mixture to the pot of a slow cooker or instant pot.
Add peppers, strained tomatoes, water, and salt. Stir to combine.
Slow cook on high in an instant pot (using the slow cook option - make sure to leave steam nozzle open) for 2 hours or in a slow cooker for 3-4 hours. The paprika chicken should fall off the bone and pull apart easily.
Remove chicken bones and skin (if you left it on), and pull chicken apart into tender chicken pieces.
Add sour cream and stir to combine.
Let slow cook on high for another 15 minutes to thicken up a bit.
If the sauce is still not thick enough for your liking, you can transfer it to a pot and let it thicken up on the stove on medium heat for a few minutes.
Serve over homemade Hungarian style dumplings or store-bought pasta.
Top with more sour cream if desired.
Enjoy!