Heat lard or butter in a large skillet over medium-high heat.
Season chicken chunks lightly with salt only and sauté until golden brown on all sides (4-5 minutes). Remove chicken and set aside.
In the same skillet, reduce heat to medium and add chopped onions. Cook until softened and translucent, about 5 to 6 minutes.
Add minced garlic and sauté for 30 seconds to 1 minute more, until fragrant.
Reduce heat to low and stir in Hungarian paprika (and smoked paprika, if using). Cook briefly (about 30 seconds), stirring constantly to prevent burning.
Add chicken broth and tomato paste, whisking gently until well combined.
Return the browned chicken chunks to the skillet. Cover and simmer gently for 15-20 minutes, until chicken is tender and cooked through.
In a small bowl, whisk sour cream with flour (if using, to thicken). Stir in a few spoonfuls of hot cooking liquid from the pan to loosen the mixture.
Pour the mixture into the skillet, stirring gently. Simmer uncovered for another 3-5 minutes until sauce thickens.
Adjust salt and pepper to taste.
Serve hot, garnished with freshly chopped parsley.