Cut the veal kidneys into pieces, discarding any fat. If using lamb’s kidneys, remove the central core by cutting a V-shape from the middle of each kidney. Cut each kidney into three or four pieces.
In a large frying pan, melt the butter with the oil over a high heat and swirl to blend.
Add the kidneys and saute for about 3-4 minutes, stirring frequently, until well browned, then transfer them to a plate using a slotted spoon.
Add the mushrooms to the pan and saute for 2-3 minutes until golden, stirring frequently.
Pour in the chicken stock and brandy, if using, then bring to the boil and boil for 2 minutes.
Stir in the creme fraiche or double cream and cook for about 2-3 minutes until the sauce is slightly thickened.
Stir in the mustard and season with salt and pepper, then add the kidneys and cook for 1 minute to reheat.
Scatter over the chives before serving.