Preheat oven to 400°F.
In a small bowl, combine kosher salt, sage, garlic powder, onion, powder, and ground black pepper. Set aside.
Trim the pork tenderloin of any excess fat and silverskin. Pat the pork dry, rub with 1 tablespoon of olive oil; rub seasoning mixture on all sides of the meat.
Heat remaining 2 tablespoons of olive oil in a large oven-safe skillet over medium heat. When the oil shimmers, add pork; cook until browned on all sides, about 4-5 minutes total.
Place butter, garlic, and rosemary in the skillet around the tenderloin. Transfer the skillet to the oven, uncovered, and bake until a thermometer inserted in the thickest portion of the meat registers 140°F - 145°F, about 8-13 minutes. Baste with the butter mixture and pan juices.
Let the pork rest at room temperature for at least 5-10 minutes. Slice into rounds and drizzle with additional garlic and rosemary-infused butter and cooking juices.