Heat a griddle on medium-high heat. Cook the poblano peppers until all sides are charred (about 15-20 minutes), turning every few minutes. *See notes for broiling method.
Seal the charred peppers in a plastic bag, and let rest for about 15-20 minutes.
Meanwhile, prepare the flour mixture. In a large shallow bowl, combine flour, salt, pepper, oregano, and garlic powder. Set aside.
Remove the chiles from the bag, and peel the skin off.
Slice a vertical line down one side of each chile, starting from the stem down to the tip.
Remove the seeds with a spoon or your hand. (Optional but recommended: Use a disposable glove if touching the seeds with your hand!)
Stuff each pepper with about ¼ cup of queso fresco, then 1 heaping tablespoon of diced onion, and ¼ cup of shredded mozarella (or white cheese of choice).
Gently squeeze the seams together to close the peppers. *See notes about using toothpicks
In a large bowl, add egg whites and use a handheld mixer to whip until fluffy and soft peaks have formed.
Add the egg yolks and whisk until just combined. Set aside.
Pre-heat a large skillet on medium-high heat, with about 1.5" of oil for frying.
Place a stuffed pepper in the bowl of flour-mixture. Rub and pat the flour mixture on the pepper until completely coated (keeping the seam closed).
Carefully dip the floured pepper into the egg-mixture, making sure to hold it closed the whole time. Once coated all around, lay it in the frying pan.
Repeat, with the rest of the peppers. (You can fry about 3 at a time in a large pan.)
Fry the peppers until they are golden brown on both sides, about 3 minutes per side.
Ready to serve!