Mix together all dry rub ingredients in a small bowl.
Use paper towels to pat the backstrap dry.
Rub the dry rub over all sides (you can do this 40 minutes or up to 24 hours in advance - refrigerate it uncovered). If you can’t rub on the seasoning at least 40 minutes before cooking, put it on immediately before cooking. Otherwise, juices will be lost, making it more difficult to sear the meat properly. If you refrigerate it, remember to let it sit at room temp for 1 hour before cooking.
Preheat the oven to 375 °F (190 °C).
Before cooking, use paper towels to again pat the meat dry. The drier the meat, the better the crust you’ll get while searing.
Get out a cast iron skillet that's large enough for the backstrap and can also be placed in the oven.
Heat it over high heat until piping hot.
Add the oil, swirl it around, and when it starts to shimmer, add the meat to the pan.
Sear the backstrap over medium-high or high. All stoves are different - if you’re on high and it’s burning, turn it to medium-high. Once there's a crust, usually after about 2-3 minutes, flip and continue searing all sides of the meat. If you try to turn it and the meat isn’t easily coming off of the pan, that means it’s not ready.
Place the skillet with the meat in the oven and cook for 5-10 minutes. It should only be cooked to 120-130 °F (49-54 °C) and will rise in temperature to about 130-135 °F (54-57 °C) - this is medium-rare - as it rests out of the oven. It's very important not to overcook it as it'll turn tough.
Remove the pan from the oven and remove the meat to a plate. Let the meat rest for about 5-15 minutes or until it reaches 130-135 °F (54-57 °C).
Meanwhile, put the pan (with the pan drippings) back on the stove at medium-low heat and add all the garlic butter ingredients. Use a wooden spatula to deglaze the pan (scrape up the flavorful bits stuck to the bottom of the pan). Cook until the garlic is soft, about 1-3 minutes.
Serve the sauce over the meat. Garnish with parsley and cut into 1 to 1.5” medallions and serve.
Let leftovers cool completely and then refrigerate in an airtight container for up to 2 days.