Lightly roast pecan pieces evenly in a 300 degree oven. Allow to cool and place in a food processor. Pulse until they are still coarse, but not fine like bread crumbs. Combine with Kosher salt and next 3 ingredients and mix well. Transfer mixture to a shallow bowl or plate.
Season venison tenderloins with salt and pepper. In a small bowl, combine Dijon mustard with Tabasco. Rub mustard mixture over tenderloins. Press tenderloins into pecan mixture and roll to coat evenly.
Heat oil in a large skillet over medium heat. Place tenderloins in skillet and brown on each side, about 5 – 6 minutes total cooking time. Allow to rest for 3 – 4 minutes and carefully slice each tenderloin into 4 medallions.