Heat the oven to 425 degrees.
Combine the rosemary, cinnamon, ginger, salt, nutmeg, orange zest and a few grinds or fresh black pepper in a small bowl, making sure to break up the clumps of zest. Mix in the oil to form a paste.
Pat the tenderloin dry with paper towels and slice away the silver skin (see notes) and any excess fat. Cut the pork in half crosswise.
Coat the pork with the paste, getting it on all sides and the ends.
Meanwhile, heat an oven-safe 10" nonstick skillet over medium heat. Add the pork and cook for 4-5 minutes per side, until browned (you may need a splatter guard for this).
Slide the skillet into the oven (removing the splatter guard first, if using) and cook until it reaches 145 degrees, about 5-7 minutes depending on its thickness. If you do not have a thermometer, aim closer to the 5 minute side, as most tenderloins are small enough that they cook quickly. It should have a slight blush in the middle and will continue to cook as it rests.
Remove from the oven and let rest for 5-10 minutes, covered loosely with foil. Slice and plate up. Taste the drippings left over from where it rested - if they're not too salty, drizzle those over the slices.