Important: Make sure your tenderloin has been setting at room temperature for at least one hour and up to two hours.
Preheat oven to 500°F (260°C). Make sure the oven rack is in the middle of the oven. Line a sheet pan with aluminum foil and spray with cooking spray.
Trim and remove the silver skin from the beef. Tie it with butcher's twine, tucking the thin end under to make the whole roast and even thickness. I usually remove the thickest end and use it another time, or I cut off the "wings" so it is a more uniform log.
Combine the mustards, balsamic vinegar, salt and pepper in a small bowl. Slather it on the meat, making sure to coat all sides. (I use my hands for this.) Place on baking sheet and grind black pepper (to taste, at least 1 tsp) over the top. Note: It is fine to use only one kind of mustard if you don't have both kinds, but make sure it is Dijon mustard either way.
If using a probe thermometer, insert it into the middle of the middle of the tenderloin and place in the oven. Set thermometer to 125°F (51.7°C) and wait for the thermometer to beep, which should take approximately 25 minutes for medium rare. If you are not using a probe thermometer, start checking the roast after 20 minutes, and at 3-5 minute intervals after that.
When meat has reached the desired temperature, remove from the oven. Cover with foil and let it rest for 10-15 minutes. Slice and serve with the horseradish sauce.