In a small bowl, combine kosher salt, sage, garlic powder, onion powder, and ground black pepper. Set aside.
Pat the turkey tenderloins dry, rub each with about 1 tablespoon of olive oil; rub seasoning mixture on both sides of the meat.
Heat remaining 2 tablespoons of olive oil in a large skillet over medium heat. When the oil shimmers, add turkey; cook until browned on both sides, about 2-3 minutes per side. Transfer the turkey to a slow cooker.
Place butter on top of and around the turkey. Arrange the garlic cloves and the rosemary in the slow cooker around the turkey.
Cover and cook on LOW for 3-4 hours or on HIGH for 1-2 hours, or until the turkey registers at least 165°F in the center when measured with an instant read thermometer.
Optional: transfer the turkey to a large rimmed baking sheet. Preheat the broiler on HIGH. Baste or drizzle the garlic butter sauce from the slow cooker on top of the turkey. Place under the broiler for a few minutes, just until browned and slightly crispy on top. Keep a close eye on the meat while it’s under the broiler, since it can burn quickly.
Let the turkey rest for about 10 minutes before slicing and serving.