Preheat oven to 375 degrees F. Spray 8 x 11″ or 9 x 13″ baking dish with cooking spray or grease with shortening.
Stir together chopped brisket, 1 cup cheese, 1/2 cup BBQ sauce, and sour cream.
Spoon the meat mixture down the center of each tortilla, roll closed, and place each enchilada seam-side down in the prepared dish. (Place rolled enchiladas close together in the pan to keep them from unrolling.)
Pour about 1/2 cup more BBQ sauce over the enchiladas in the pan. Use a basting brush or spoon to spread the sauce evenly over the enchiladas. Cover with foil and bake in preheated oven for 35 minutes.
Remove foil, spread remaining 1 cup of cheese over the enchiladas. Drizzle a little more BBQ sauce over the cheese. Return to oven and bake 8-10 minutes longer until cheese is melted.