Prepare the Backstrap: Trim any silver skin or excess fat from the wild boar backstrap. Pat dry with paper towels.
Marinate the Meat: Rub the backstrap with olive oil, minced garlic, chopped rosemary, thyme, salt, and pepper. Let it marinate for at least 30 minutes (or overnight for best flavor).
Cook the Backstrap: Pan-Seared: Heat a cast-iron skillet over medium-high heat, add olive oil, and sear the backstrap for 2-3 minutes per side until browned. Lower heat and cook for 2-3 more minutes for medium-rare.
Grilled: Preheat the grill to medium-high heat, and grill the backstrap for 3-4 minutes per side for medium-rare.
Finish with Butter (optional): If pan-searing, add butter to the skillet and cook for an additional 2-3 minutes, basting the meat with the melted butter.
Rest the Meat: Let the backstrap rest for 5-10 minutes before slicing.
Serve: Slice into medallions and serve with your favorite sides.