Place the tenderloin medallions between sheets of plastic wrap or wax paper with the cut surfaces facing up and down. Pound the medallions into cutlets about 1/4 to 1/8 of an inch thick. Cut small slits on the edges of the cutlets so they won't curl when cooked.
Season the half-cup flour with salt and pepper. Combine the egg and milk. Season the breadcrumbs with paprika. Dredge the cutlets first in the flour, then the egg bath then the seasoned breadcrumbs.
In a large skillet, cook 3 cutlets at a time in hot shortening, 2-3 minutes on each side. Remove the cutlets from the pan, set aside and keep warm.
Drain excess grease from pan. Return to heat and add butter and shallots. Sauté for about a minute.
Deglaze pan with white wine, scraping to loosen browned bits from the bottom of the pan. Once wine is almost completely evaporated, add chicken stock and return to a boil.
In a small bowl, stir one tablespoon flour and the dill weed into the sour cream then stir the sour cream mixture into the broth.
Stir and reduce over medium heat until thickened and bubbly.
Serve the cutlets on a warm platter garnished with fresh dill. Pass the sauce separately.