Preheat a gas burner or grill. Roast the 6 poblanos directly over the flame, turning them with tongs until the skin is evenly brown, charred, and bubbling on all sides.
Transfer the hot poblanos to a plastic bag, seal it, and let them sweat for 10 minutes.
Remove the peppers from the bag. With your fingers or a small knife, peel off the charred outer skin. Make a small lengthwise incision in each pepper and carefully remove seeds and membranes, keeping the flesh as intact as possible. Pat the peppers dry with paper towel and set aside.
Slice the Oaxacan cheese and Queso Fresco into thin strips. Use equal amounts of each cheese and divide the strips among the 6 peppers. Stuff each pepper with the cheese strips and close the incision as best you can.
Pour vegetable oil into a wide, heavy skillet to a depth of about 1 inch. Heat the oil over medium–medium-high heat until hot but not smoking.
Separate the 3 eggs into whites (large bowl) and yolks (small bowl). Beat the egg whites until they form soft peaks. Add salt to taste, then gently incorporate the yolks into the beaten whites until the mixture is uniform.
Put the 1/3 cup unbleached all-purpose flour on a plate. Lightly dust each stuffed pepper with flour, shaking off any excess.
Using a perforated spoon, slotted spatula, or tongs, dip each floured pepper into the egg mixture and turn it so the pepper is evenly coated.
Test the oil by dropping a small bit of batter into it; when it sizzles and froths, the oil is ready. Fry the coated peppers in batches, lowering them carefully into the oil and turning as needed, until the batter is set and deep golden on all sides (work quickly so they brown evenly).
Transfer fried chiles to a plate lined with double paper towels to drain excess oil.
Sprinkle the finished chiles with cotija cheese and chopped cilantro. Serve immediately.