Preheat the oven to 350 °F
While the oven is heating, pat the pork tenderloin dry. Salt and pepper the pork tenderloin on all sides.
Heat olive oil in an oven safe skillet or cast-iron skillet. Once the oil shimmers, carefully add the tenderloin. I use a splatter screen over the top of my pan. This stops the spitting oil but doesn't trap moisture like a lid which will ruin your sear.
Sear each side for 2 minutes, do not move the tenderloin. Flip and repeat for 1 minute on the remaining raw sides. If there is fat strip on the tenderloin, it should be at the top when finished searing. You may have to hold the tenderloin in place on the long, narrower sides with tongs if it doesn't stand up on its own. The ends should not need to be seared.
Remove the skillet from the heat. Add butter, garlic, and rosemary to the pan. Spoon the butter and oil mix over the tenderloin.
Place the oven safe skillet on the middle rack in the oven.
At 5-minute intervals, spoon the oil-butter mix over the tenderloin. Bake for 15 minutes or until the internal temperature at the thickest point is 145℉, the center will be slightly pink, but done. You'll be able to see the grain of the meat. Allow the tenderloin to cook for longer until the internal temp is between 150℉ to 160℉ to get a more well-done center.
At the end of the cooking time, remove the tenderloin from the pan and on to a serving plate. Let it rest for 5 minutes before slicing.