Roast the Poblanos
Place the poblano peppers directly over a gas flame, on a hot comal, or under the oven broiler.
Turn occasionally until the skins are blistered and charred on all sides, approximately 8 to 12 minutes depending on the method.
The goal is to loosen the skins while softening the peppers enough to make them pliable.
Steam the Peppers
Transfer the roasted poblanos to a covered bowl and let them steam for 10 minutes.
Once cool enough to handle, gently rub away the blistered skins.
Avoid rinsing under running water if possible, since that can wash away some of the roasted flavor.
Remove the Seeds
Carefully cut a slit down one side of each poblano.
Remove the seeds and thick inner membranes while keeping the pepper as intact as possible.
Leave the stem attached if you can.
Stuff With Cheese
Divide the Oaxaca cheese evenly among the six peppers.
Gently close the openings around the filling.
If necessary, secure each pepper with one or two wooden toothpicks. Remember to remove them before serving.
Prepare the Tomato Caldillo
Blend the tomatoes, onion, garlic, and broth until smooth.
Heat 1 tablespoon oil in a saucepan over medium heat.
Carefully pour in the blended mixture.
Add the Mexican oregano, salt, and black pepper.
Bring to a gentle simmer and cook for 15 to 20 minutes, stirring occasionally, until the raw tomato flavor has mellowed and the sauce is slightly reduced.
Taste and adjust seasoning.
Keep warm over low heat.
Prepare the Egg Batter
Separate the eggs, placing the whites in a clean, dry mixing bowl.
Beat the egg whites with an electric mixer until stiff, glossy peaks form.
Lightly beat the yolks with the salt.
Gently fold the yolks into the whipped whites, taking care not to deflate the mixture.
Work promptly because the batter gradually loses volume.
Dust the Peppers
Pat the stuffed poblanos dry with paper towels.
Lightly coat each pepper with flour, shaking off the excess.
This helps the egg batter adhere.
Heat the Oil
Pour enough neutral oil into a heavy skillet to reach approximately ½ inch deep.
Heat to around 350°F.
The oil should be hot enough to puff and set the batter without burning it.
Coat and Fry
Working with one or two peppers at a time, gently coat each stuffed poblano in the egg batter.
Carefully lower it into the hot oil.
Fry for approximately 2 to 3 minutes per side, turning gently, until the coating is puffed, golden, and cooked through.
Adjust the heat as needed to maintain a steady frying temperature.
Drain
Transfer the fried chiles rellenos to a wire rack set over a baking sheet or to a paper towel-lined plate.
Allow excess oil to drain.
Repeat with the remaining peppers.
Assemble
Spoon warm tomato caldillo onto individual plates.
Place one chile relleno over the sauce.
Add a little more caldillo around the pepper if desired.
Serve
Serve immediately while the coating is golden and the cheese is warm and melted.
Mexican rice, beans, and warm corn tortillas make excellent accompaniments.