Blend together the mustard and 3 tablespoons of the butter and set aside.
Remove any fat and opaque membrane from the kidneys without piercing the flesh. Kitchen scissors work best for this.
Over medium heat melt the remaining 3 tablespoons butter in a medium skillet until the foam begins to subside.
Roll the kidneys in the melted butter, then cook them uncovered for about 10 minutes, turning every minute or two. Regulate the heat so that the butter is always very hot but not discoloring. The kidneys should brown lightly and stiffen but not become hard.
Remove them from the skillet and keep warm for the few minutes it takes to make the sauce.
Stir the shallots into the butter in the skillet and cook for about one minute. Add the wine and the lemon juice. Boil, scraping up the cooking juices and reduce the liquid to about 4 tablespoons.
Off heat swirl in the mustard/ butter mix by spoonfuls into the skillet.
Cut the kidneys into slices 1/8 inch thick (they should be a light pink). Sprinkle with salt and pepper.
Toss the kidney slices in the skillet with their juices and the parsley over low heat for a minute or two to warm them without allowing the sauce to simmer.