Using a small, sharp knife or kitchen shears, remove the gristly pelvis from each kidney.
Toss flour, salt, pepper and cayenne to combine. Dredge kidneys in seasoned flour, shaking well to remove any excess.
Melt butter in a large skillet over medium-high heat. When melted, add kidneys in one layer. Cook until browned on both sides, about 2 minutes on each side.
Add Dijon mustard, Worcestershire sauce and chicken stock to pan, whisking to combine. Simmer until kidneys are tender, about 2 minutes more. Remove kidneys to a warm plate and tent with foil.
Continue simmering sauce until reduced by about half, until sauce coats the back of a spoon. Adjust seasoning with salt and pepper as desired. Slice each kidney in three pieces on the bias and place on top of toasted bread. Spoon sauce over kidneys and sprinkle with parsley to serve.