This recipe is really all about the sauce, so the fact that I use venison here is incidental. Beef would be traditional in Argentina, where chimichurri comes from, but lamb, goat or even pork would be fine, too. I use wild mint, but you can use whatever mint you want. You can also play with proportions, too. Hate mint? Use oregano. Use fresh herbs when you can, but when you can't find them, dried parsley, chiles and mint work fine.
Food processor method: Put the garlic, herbs, chile, lime juice and a little salt in the bowl of a food processor. Buzz to combine, but do not puree. With the motor running, drizzle in the olive oil. Add more salt and black pepper to taste. Let steep for an hour or so before serving.
Traditional method: Mince the garlic, chile and herbs by hand and pound a little in a mortar and pestle. Add the lime juice, salt and pepper and then mix in the olive oil slowly by hand, stirring all the while. Let steep for an hour or so before serving.
For the venison: Take the meat out and let it come to room temperature. Pat it dry with a paper towel, then coat with the vegetable oil. Salt it well.
If you are grilling, get your grill hot and clean the grates. If you are planning on pan-roasting, preheat your oven to 400 degrees Fahrenheit and get a large saute pan hot on your hottest burner.
Grill the venison, turning occasionally until it is medium-rare, or however you like it; this should take about 10-15 minutes. If you are pan-roasting, brown the outside of the venison backstrap in the saute pan, then put the whole pan into the oven. Roast for about 8 minutes for rare. Use the finger test for doneness as your guide.
Let the venison rest on a cutting board. Right before you slice and serve it, Pour any accumulated juices into the chimichurri. Pour the chimichurri over the sliced venison and serve at once.