For the tenderloin: Preheat the oven to 400 degrees F. Remove the meat from the refrigerator 30 minutes before cooking.
Heat a large skillet over medium-high heat. Dry the meat well and sprinkle with the salt. Add the oil to the pan along with the rosemary sprigs. Add the meat and sear until deep golden brown all around, 3 to 4 minutes per side. Remove the meat to a rimmed baking sheet fitted with a baking rack. Roast until an instant-read thermometer inserted in the thickest part reads 125 degrees F, 35 to 50 minutes. Allow the meat to rest for 15 minutes before slicing.
For the peperonata: Meanwhile, place the skillet that you seared the meat in over medium heat. Add the garlic and anchovy paste and cook, stirring with a wooden spoon, to bring out the flavors, for 1 minute. Add the onion and cook for 2 minutes. Add the peppers and salt and cook, stirring occasionally, until the onions are caramelized and the peppers are soft and beginning to brown, about 6 minutes. Stir in the olives, vinegar, capers and oregano. Remove from the heat.
Spoon the peperonata onto a platter. Slice the tenderloin and shingle it around the platter. Sprinkle the meat with the coarse salt if using and drizzle with any juices.