Preheat the oven to 425 degrees F. Rub the tenderloin down with the oil, salt, pepper, and rosemary, then refrigerate.
Combine the apricots and lemon juice and season to taste with salt and pepper.
Heat an oven-safe skillet over medium-high heat and add some olive oil to the pan. Sear the tenderloin for 3-4 minutes on each of at least two sides. You can do all four if you want, but that isn't necessary.
Brush the tenderloin with a bit of the apricot glaze and bake 5 minutes before rotating and brushing again. Repeat every 5 minutes until the internal temperature reaches 145 degrees F. This usually takes about 20 minutes.
Let the pork rest for 10 minutes before serving topped with any remaining glaze.