Cut a slit in the venison backstrap (lengthwise), leaving it connected on one side. Open up the meat and cut several more slits in the thicker part of the meat to make it lie flat. Pound flat with a meat tenderizer mallet.
Heat grill to 400, place flattened backstrap on grill just long enough to get a bit of a sear on one side. Do not flip meat!
Mix cheddar, green Chile and cream cheese together. Place meat on flat surface, and spread the cheese mixture down the center pf the seared side of the meat.
Roll meat into a log, and secure with kitchen twine at 1-inch intervals. Tie the ends tightly to keep filling inside.
Place stuffed backstrap on grill, turning occasionally till all sides are browned. When a meat thermometer inserted into the meat reads 130, brush all side of backstrap with BBQ sauce and continue grilling until the internal temp reads 145. Remove from heat, let rest 5-10 minutes, and serve!
Notes
You may use toothpicks to secure meat if you don't have twine. (Twine can be found in most grocery stores near the kitchen tools section.)You can add jalapeños for some heat, or use different kinds of cheeses if desired. Elk, deer, or antelope work great for this recipe!