Heat olive oil in a pot. Blend the next 6 ingredients together in a small bowl. Whisk broth and tomato paste together in another bowl. Add dry ingredients to hot oil and whisk to bubble and “cook” the flour. Slowly stir in the broth mixture and simmer over medium high heat for about 5-7 minutes until the sauce begins to thicken. Remove pot from heat and stir in vinegar, black pepper (and pinch of additional salt if needed) to taste. Set aside.
Heat oven to 375. Coat a 13x9 inch baking dish or foil pan with cooking spray. Spread a thin layer of enchilada sauce (about ½ cup) in the dish. Brown venison in a skillet then stir in about ½ cup of enchilada sauce and can of chiles. Divide meat evenly into flour tortillas and sprinkle with cheese. Wrap tortillas around meat and cheese filling, place each in the baking dish with the seam side down. Cover with remaining sauce and a layer of cheese. Bake 20-25 minutes until bubbly and cheese topping is browned. Rest about 5 minutes before serving.