Roast the peppers over an open flame, or use your oven broiler, until skins are blackened on each side. Over flame, it should only take about 5 minutes. In the broiler, it could take 10 or more minutes.
Remove the peppers and transfer to a paper or plastic bag and seal them up. Allow to steam and cool. This will loosen up the skins.
Once cooled, peel off the blackened skins.
Slice open each pepper lengthwise with one long slit, then remove the innards with a knife or spoon.
Stuff each pepper with cheese, but do not overstuff. Make sure you can still close the pepper.
Heat 2 inches of vegetable oil in a wide pot to 375 degrees F. Do not let the oil boil. If you do not have a thermometer, test the oil with a tiny drop of flour. It will immediately sizzle up.
Separate the egg yolks from the whites and add the egg whites to a large bowl. Beat the egg whites until they fluff up and form stiff peaks, about 5 minutes. An electric egg beater is ideal. Gently stir in egg yolks.
Add flour to a separate bowl with a bit of salt. Dip the stuffed peppers into the flour to coat them, then dip them into the egg batter to coat them completely.
Fry each pepper about 2-3 minutes each side, or until they are a golden brown.
Remove the peppers and set them onto a paper towel lined plate to drain excess oil.
Serve with your favorite salsa or sauce!