In a medium saucepan combine undrained chile peppers and the chili powder; cook about 1 minute or until heated through. Stir in flour. Cook and stir for 1 minute more. Remove from heat. Stir in sour cream and 1/2 cup of the cheese.
Preheat oven to 350 degrees F. Grease a 3-quart rectangular baking dish; set aside. Divide beef among tortillas. Top with sour cream mixture. Roll up tortillas. Arrange rolled tortillas, seam sides down, in prepared baking dish.
Cover with foil. Bake for 30 minutes. Uncover. Sprinkle with half of the remaining cheese. Spoon salsa verde over enchiladas; sprinkle with remaining cheese. Bake, uncovered, about 10 minutes more or until cheese is melted and enchiladas are heated through.