Remove the thin outer membrane of the kidneys, and then cut the kidneys in half lengthwise. Set the kidneys in a large bowl, and cover them in enough cold water to submerge them entirely. Add 1 Cup of Red Wine Vinegar to the bowl. Allow the kidneys to soak for ~15 minutes, to remove any odor. After ~15 minutes, rinse them thoroughly under a flowing faucet, then dry them off well with a paper towel.
Finely chop the shallot, and place it in a small bowl to the side. Finely chop the parsley, and place it ima separate small bowl off to the side.
In a medium or large pan, over medium-high heat, melt 1 Tbsp of butter. Once the butter is mostly melted, add 1 Tbsp of Vegetable Oil. Once the pan is extremely hot, just about smoking, place in the kidneys. Season them with salt and pepper. Sear the kidneys on both sides until nicely browned on the outside, but still pink within. Once finished, remove them from the pan and set them on top of a few paper towels to drain.
Wipe out the pan with a paper towel, and then return it to medium heat. Add 1 Tbsp of butter, then add the shallots. Stir frequently for several minutes, until the shallots are soft with no color. Pour over a splash of Cognac, and stir the bottom of the pan to loosen any stick flavor. Add 5 fl oz of Demi Glace, and reduce just a bit. Add 2 fl oz of heavy cream. Cook and stir for ~10 minutes, until reduced to a sauce-like consistency.
Take the pan off the heat, and add 1 Tbsp (or to taste) of Dijon mustard. Season the sauce with salt and pepper. Stir the sauce, and return the pan to a low heat. Add the kidneys to the pan. Heat them through and coat them with the mustard sauce.
Transfer the kidneys and sauce to a warm serving platter. Sprinkle with the finely chopped parsley, and serve!