Make the marinade. In a medium bowl, whisk together melted butter, 1 tablespoon olive oil, apple cider vinegar, brown sugar, minced garlic, thyme, rosemary, paprika, salt, and pepper until well combined.
Marinate the turkey. Add turkey tenderloins to the bowl and coat them completely in the marinade, turning to cover all sides. Cover the bowl and refrigerate for at least 30 minutes or up to 24 hours. (The longer it marinates, the more flavorful it becomes.)
Preheat the oven. When ready to cook, preheat your oven to 400°F.
Sear the turkey. Heat an oven-safe skillet (cast iron works great) over medium-high heat. Add the remaining 1 tablespoon of olive oil and swirl to coat the bottom of the pan. Use tongs to transfer the marinated turkey tenderloins to the hot skillet. Sear for 2-3 minutes per side without moving them, until golden brown and caramelized.
Bake the turkey. Transfer the skillet directly to the preheated oven. Bake for 17-20 minutes for 1/2 lb tenderloins, or 25-30 minutes for 1 lb tenderloins. The internal temperature should reach 160°F in the thickest part.
Rest before serving. Carefully remove the skillet from the oven (it will be very hot!). Tent the turkey loosely with aluminum foil and let it rest for 10 minutes. The internal temperature will rise to 165°F as it rests.
Slice and serve. Check that the internal temperature has reached 165°F, then slice the turkey into medallions and serve with your favorite sides.