In a small bowl, whisk together 3 tablespoons oil and mustard; set aside.
Rub remaining 1 tablespoon oil all over pork; rub salt, black pepper, and cayenne all over pork. Let stand for 10 minutes.
Heat a 12-inch cast-iron skillet over medium-high heat until hot and smoking. Reduce heat to medium. Add pork, and cook, turning frequently, until browned on all sides, about 10 minutes. Brush pork with mustard mixture.
Bake until an instant-read thermometer registers 145°, about 15 minutes, or to desired degree of doneness. Remove from skillet, and let stand for 10 minutes. (Do not cover as it will sweat off the coating.) Slice and serve with Champagne Vinaigrette and chopped arugula. Garnish with arugula, if desired.
Champagne Vinaigrette
In a small bowl, whisk together all ingredients. Use immediately.
Recipe by Louisiana Cookin' at https://louisianacookin.com/peppery-pork-tenderloins-mustard-glaze/