When I want to please a crowd but don’t have a lot of time, this is one of my go-to recipes. Blending olives and mushrooms makes a tapenade-like spread that I can prepare ahead, and I love how the salty olives contrast with the mild pork tenderloin. I pair this dish with simple mashed potatoes or Roasted Pear and Cranberry Brussels Sprout)—or both.
Transfer the mushroom mixture to a food processor, add the olives and capers, and pulse until coarsely chopped. You may have to pulse a few times to break up the olives. Taste, seasoning with a pinch of salt and pepper if desired (keep in mind that the olives are already quite salty). With the food processor running, drizzle in the remaining 3 tablespoons olive oil until a chunky paste forms. Set aside.
To make the pork: Preheat the oven to 450°F. Line a rimmed baking sheet with aluminum foil.
In a small bowl, combine the paprika, thyme, salt, and pepper. Rub the spices into the tenderloins.
Heat the oil in a skillet over medium-high heat. In batches, brown each side of the tenderloins until golden brown, 1 to 2 minutes per side. Place the tenderloins on the prepared baking sheet. Coat each tenderloin with a thick layer of the olive-mushroom spread and bake until cooked through, 20 to 25 minutes. If using an instant-read meat thermometer, the internal temperature at the thickest part of the tenderloin should reach 140°F. (It will continue to cook as it cools.)
Let the pork rest for at least 5 minutes or up to 15 minutes to give the juices time to reabsorb into the meat. Cut into thick slices to serve.