First - Written out recipe's aren't really my thing. I cook by feel/taste but I'll give some guidelines based on what I do...
For this recipe you NEED a good instant read thermometer. Thermapen MK4 is my suggestion. Getting internal temps correct with venison is a requirement if you want good, tender, moist, flavorful meat.
Get a 6-8" long hunk of back strap, clean it up real nice. Let it sit on the counter for an hour or so to let it come up to room temp. Coarse kosher salt and fresh ground pepper. Get a good amount of salt on there, it's a big chunk of meat.
Pre-heat the oven to 300ºF and put a foil lined pan in there.
You will want a cast iron skillet OR a black steel pan. Get it on the stove top, and get it ripping hot.
Sear that back strap on all sides. I usually give it about a minute per side with the pan on high heat.
Now put the back strap in the oven on the foil lined pan. (start the onion recipe below now in this same pan)
There is no time for this. You must check internal temps. Remove the backstrap from the oven when the temp in the very middle of the meat reaches about 125. It probably won't take long. Check it every 5 or so minutes. A leave in oven safe thermometer makes this easier if you have one.
When the internal temp reaches 125ºF, remove and tent with foil for at least 5 minutes. I usually let it rest until my onions are done. When ready, you're going to slice against the grain. The grain runs the long ways in the back strap. So cut 90º to the long side. I cut them in quarter inch medallions and plate them nicely.
Sautéed onions:
1 very large yellow onion - Julienned (
)
3 tbsp butter
1 tbsp Worcestershire sauce
Montreal steak seasoning to taste
Salt/Pepper to taste
In the pan you just seared off the back strap in, let the pan cool down so you don't burn the butter, set to a medium heat.
Add the butter, allow to melt, and scrape the frond (that's the bits of meat that are stuck to the pan) off the bottom
Add the onions, salt, pepper, steak seasoning, and Worcestershire sauce.
Cook, stirring frequently, until the onions are dark brown
With this meal we usually do either mashed or baked potatoes, but I'm confident you can figure those out