I'm going to cover two types here, firstly a poblano chile stuffed with queso fresco and secondly a jalapeño stuffed with queso oaxaca, a type of melting cheese.
These are a treat, the chile is soft and grassy with just a hint of heat and there is sharpness from the cheese, that cuts the oil. I think its best to use a queso fresco with a poblano as, given the larger size of a chile, any other cheese would be too rich.
There is nothing difficult here. The preparation is more a matter of motivation and organisation and there is certainly no difficulty, just be prepared for a lot of cleaning up! The only unusual item is the batter itself which is an egg white whipped to a stiff peak, with the yolk folded into it and stabilised with a spoonful of flour. The batter is therefore very light, it's not crispy like a tempura, neither is it dense like batters normally made with egg.
The first job is to roast the poblano. As you would do if preparing rajas.
The dough is prepared by beating the white of an egg to a stiff peak. (I don't have a mixer and have to do this with a small manual whisk, it's not actually as much of a chore as I thought it would be, although I probably stopped somewhere short of stiff peaks). When the egg whites have been beaten the yolk of the egg is folded in and I also add a tablespoon of flour just to stabilise the batter, but this is omitted in many recipes.
When the roasted peppers have been steamed and skinned, cut a slit in the side and extract the seeds and membranes and stuff the cavity with grated or crumbled queso fresco. Try and keep the slit as small as you can manage, you can use a couple of toothpicks to suture it back together after you have stuffed it, however if you work carefully there is no need as the batter will set before anything falls out.
Dust the stuffed chile with flour and then coat with the batter. Either deep fry or fry in an inch or so of corn oil.
Drain on some kitchen paper as the cooked chiles can be quite oily.
The procedure for jalapeño peppers is identical to that above, except the peppers are smaller and everything is more fiddly and infuriating!
Rather than using queso fresco though you can use a melting cheese like queso oaxaca, as the jalapeño is so much smaller and hotter than a poblano there would not be too much cheese and there is some heat to contrast the richness.