At one time these cheese-stuffed grilled chilis were my favorite appetizer at MacArthur Park Restaurant in San Francisco. At the restaurant they are made with Pasilla peppers, and stuffed with a combination of Cheddar, Jack, and Blue Cheeses. They are served with a fresh tomato based salsa with cilantro and lime.
Poblano chili peppers are more readily available where I live now, so that is what I usually use. Which ever chili pepper you choose, select ones that have smooth skins, and wide cavities so they will be easier to stuff. With a small sharp knife cut the stems out of the chilis; if you cut them as shown below, leaving the "shoulders" of the peppers intact it will help to keep the cheese inside of the peppers while grilling. (Rather than slicing them straight across.)
Reach in and remove the seeds and pith; using a knife to assist, if necessary.
I skip the blue cheese and simply stuff them with pieces of cheddar and jack (you can use any cheese or cheese that you like best.) You may secure the tops to the body of the chilis with tooth picks if they don't fit back inside securely. To grill, simply brush the chilis with oil, salt them lightly if desired, and grill until slightly charred, and the cheeses have melted.
Sometimes I serve them as an appetizer before a grilled dinner, but usually they appear as the main course as shown here. A black bean and corn salsa, Mexican-style rice and diced avocados make delicious accompaniments. A few lime wedges served alongside offer a favorful addition if you have them.
Over the years I've come to prefer this style of Chili Relleno rather than it's fat laden, egg dipped and fried cousin, the texture and flavors are fresher and more interesting to me.