Most people use the poblano or Anaheim chiles for Chile Rellenos; they are firmer and easier, but in our opinion, not as flavorful as the New Mexico Hatch chiles. This is just a little labor-intensive, but well worth it. Once you've done it a time or two you'll find the process goes quite quickly.
 

You can either cut off the tops of the chiles before stuffing them from the top, or if you wish to look more authentic in your presentation leave the tops on and make a slit in the side to stuff each chile. You probably want to remove some of the seeds from the top of the chile where they are heavily concentrated. Cut the Monterey Jack cheese into narrow finger-like strips, then insert them into your chiles. Take care, as the chiles are fragile. If they fall apart while you are working, just wrap them gently around the strip of cheese. Set the stuffed chiles aside while you heat the oil for frying.

Using a medium-size frying pan, heat approximately 1/2" or more of oil to a temperature of 375 degrees or until a drop of batter bubbles and starts to puff as soon as it hits the oil. Meanwhile, pat the chiles dry with a paper towel, turn over and pat the other side dry. Dredge it gently in flour, then drop it into the batter. Turn with a spoon to coat it thoroughly, then use a slotted spoon to lift the batter-covered chile and place it in the hot oil. Fry quickly on each side until golden in color, then remove from the oil and drain on a paper towel.

Chile rellenos can be served with a red chile sauce or a green chile sauce, or they can also be served with a tomato sauce or a salsa. Serve as main dish with beans and/or rice on the side, guacamole, lettuce and tomatoes. Leftover chile rellenos are best reheated in the oven or a toaster oven, otherwise they will be too soggy.