Somebody has blessed you with the very best cut at the best time! My own speculation is that the earlier one acquires hunted game in the season, the better...
Portion the loin into 2" wide cuts. Reserve the 'tails' for amuse' bouche. Pat them dry with paper towels. Bring your oven to 325 degrees. If you have an electric stove with a oven 'chimney' in the back left burner, place a sheet pan there. Also bring a large, deep sautee-pan lined with EVOO to just at smoking point. Salt and pepper your tenderloins and place them in the pan, taking care not to overcrowd the pan. Salt and pepper the other side. They are ready to be turned when they release from the pan without effort. Repeat on the other side. Remove from pan and let rest for 10 minutes at room temperature. This should produce a temperature just above medium-rare, ideal for wild venison. If you prefer it cooked more, place the tenderloins in the pan above the chimney- that they may gently upcook.
If you have to make multiple batches, I recommend deglazing in between. Add sliced onions, let them simmer until semi soft. Add button mushrooms and garlic and let sautee for 3-5 mins. Then add a cup or so of red wine, scraping up the crispy bits in the pan. Add another cup of stock (or water, if you have to) and bring to a boil. Add a teaspoon of corn starch slurry (1 tsp starch to 2 oz water) and then reduce heat, stirring constantly. Once thickened, pour into a gravy boat and keep on the back of the stove. Wash out your pan and begin again...
Oh yea... add chopped herbs, salt and pepper as you like!
