Step 1: Roast the Poblano Peppers. Preheat your broiler to high, or heat a cast-iron skillet over high heat. Place the poblano peppers directly on a baking sheet under the broiler or in the hot skillet. Turn them every few minutes until the skins are completely charred and blistered on all sides. This usually takes 10-15 minutes. Alternatively, you can roast them over an open flame on a gas stove.
Step 2: Steam and Peel the Peppers. Once charred, immediately transfer the hot peppers to a bowl and cover tightly with plastic wrap or place them in a paper bag and seal. Let them steam for 15-20 minutes. This helps loosen the skins. Once cooled enough to handle, carefully peel off the charred skin using your fingers or a paring knife. Make a slit down one side of each pepper, from the stem to the tip, and gently remove the seeds and membranes. Be careful not to tear the pepper too much, as you’ll need it to hold the filling.
Step 3: Prepare the Cheese Filling. Cut your Oaxaca or Monterey Jack cheese into sticks or blocks that will fit snugly inside the peppers. Stuff each peeled and seeded poblano pepper with a generous amount of cheese. If you like, you can secure the opening with toothpicks, though often this isn't necessary if the peppers are well-stuffed.
Step 4: Make the Tomato Sauce. While the peppers are steaming, prepare your sauce. Heat a tablespoon of olive oil in a saucepan. Sauté 1/2 chopped onion and 2 minced garlic cloves until fragrant. Add a 15-ounce can of crushed tomatoes, 1/2 cup chicken broth, 1 teaspoon cumin, and salt and pepper to taste. Simmer for 15-20 minutes, allowing the flavors to meld.
Step 5: Prepare the Egg Batter. Separate the egg whites from the yolks into two clean, dry bowls. Beat the egg whites with an electric mixer on high speed until stiff peaks form (they should hold their shape). In the bowl with the yolks, whisk them lightly with the salt. Gently fold the whisked egg yolks into the stiff egg whites until just combined. Don't overmix!
Step 6: Dredge and Batter the Peppers. Place a thin layer of all-purpose flour on a plate. Dredge each cheese-stuffed poblano pepper in the flour, shaking off any excess. This helps the egg batter adhere. Carefully dip each floured pepper into the egg batter, ensuring it’s completely coated.
Step 7: Fry the Chile Rellenos. Heat about 1 inch of vegetable oil in a large, deep skillet or Dutch oven to 350-375°F (175-190°C). Carefully place one or two battered peppers into the hot oil (don't overcrowd the pan). Fry for 2-3 minutes per side, or until golden brown and puffed. Use tongs or a slotted spoon to carefully turn them.
Step 8: Drain and Serve. Remove the fried chile rellenos from the oil and place them on a plate lined with paper towels to drain excess oil. Repeat with the remaining peppers.
Step 9: Serve. Spoon warm tomato sauce onto plates, then place one or two chile rellenos on top. Garnish with fresh cilantro or cotija cheese, if desired. Serve immediately with Mexican rice and refried beans.