Melt butter in a large skillet over low heat. Stir ham strips and onion slices with the melted butter; season with black pepper. Cook and stir the mixture until the onion is tender, 5 to 7 minutes.

Sprinkle flour over the ham mixture and stir; add sour cream and mushrooms and cook, stirring continually, until the liquid thickens and the mushrooms are heated through, about 15 minutes.

Divide rice between four plates. Ladle the ham mixture over rice; garnish with parsley.