Preheat oven to 375 °F
Prepare the backstrap: Pat the venison dry with paper towels. Season generously with salt and pepper on all sides. Let it rest at room temperature for 20-30 minutes before cooking.
Sear in cast iron: Preheat a cast iron skillet over medium-high heat until hot. Add olive oil. Place Backstrap in the skillet and sear for 2 - 3 minutes per side, until a golden brown crust forms. Toss in garlic and rosemary to infuse flavor. Add a pat of butter on top of each piece before transferring to the oven.
Finish in the oven: Transfer the skillet to a preheated 375℉ oven. Roast for 10 - 15 minutes, depending on thickness and desired doneness (135℉ for medium-rare is perfect for venison).
Rest and slice: Remove the backstrap from the oven and let it rest, loosely covered with foil, for 10 minutes. Slice against the grain into medallions and serve warm.