Place the the fillets in a gallon size ziplock bag with the shallot oil, salt, and pepper. Remove the air, seal the bag, and refrigerate for 2 hrs up to overnight.
When you’re ready to cook them, preheat your oven to 425 degrees.
Heat an ovenproof skillet or sauté pan over medium-high heat (I prefer our cast iron skillet). Add the entire oil marinade to the skillet and allow it to get hot.
Add the filets to the skillet and cook for 4 minutes. Flip the filets and transfer the sauté pan to your pre-heated oven. Cook for 5-7 minutes: 5 minutes for rare, 6 minutes for medium-rare, or 7 minutes for medium.
Remove from the oven and check the temperature (general guidelines: 120-125 degrees for rare, 130-135 for medium rare, and 140-145 for medium. Remove them from the oven on the lower end of the scale as they will continue to cook even after out of the oven).
Put the filets on a plate and let rest for five minutes before serving. Do not leave them in the skillet or they will overcook.
Spoon any juices from the sauté pan over the filets and serve immediately with crispy fried shallots on top.