Preheat the oven to 350 degrees. In a medium bowl, combine the beef, 1/2 cup enchilada sauce, 1/4 cup cooking liquid and all but 1 tbsp. of the cilantro.
Arrange the tortillas on a work surface. Divide the rice among the tortillas, then top with the beef mixture. Roll up the tortillas, then line them up, seam side down, in a 1 1/2-qt. baking dish. In a medium bowl, mix the remaining cooking liquid with the remaining enchilada sauce; pour over the enchiladas. Sprinkle with the cheese.
Bake the enchiladas until the sauce is bubbly and the filling is heated through, about 20 minutes. Sprinkle with the remaining 1 tbsp. cilantro.