Prepare the venison: Remove the venison loin from the refrigerator and allow it to come to room temperature for about 30 minutes before cooking. Pat dry with paper towels and season generously on all sides with salt and freshly cracked black pepper.
Sear the venison: Heat olive oil in a cast iron skillet or heavy-bottomed pan over medium-high heat. Once hot, add the venison loin and sear on all sides until a golden-brown crust forms.
Cook to desired doneness: Continue cooking until the venison reaches your preferred internal temperature. For tender, juicy venison, medium-rare (about 130–135°F) is often recommended. Avoid overcooking, as venison is very lean and can become dry.
Rest the meat: Remove the venison from the skillet and allow it to rest for 5–10 minutes before slicing.
Finish with herb butter: Slice the venison and top with rosemary garlic compound butter. Allow the butter to melt over the warm meat before serving.