If your oven is not already on, preheat to 400 degrees.
Remove any silver skin, tendons, or things that look like they don't belong from the meat. Generously salt with coarse Kosher salt and freshly ground black pepper. If you're not cooking right away, cover with plastic wrap and place in the refrigerator until ready to cook. Remove from the fridge and bring to room temp before sauteing.
Heat the butter in a heavy bottomed skillet until it foams up. Gently add the venison tenderloins to the pan. Try not to overcrowd as you will need room for basting.
Generously baste each piece of meat with the butter by spooning it up over the meat. Cook for about 3 to 5 minutes or until a nice crust forms on the bottom.
Turn the tenderloins over and repeat the basting process for another 3 to 5 minutes.
Place in a hot 400 degree oven for 10 to 15 minutes.
Use a meat thermometer to test doneness. 130 - 135 degrees is rare to medium rare. Alternatively press your thumb into the meat. Rare will feel soft like the fleshy area at the base of your thumb. I prefer the meat thermometer...more accurate.
When done, remove from the oven, tent the tenderloins with foil and let rest for another 10 minutes before cutting into 1 1/2 to 2 inch slices.
