Step 1: Roast the poblano peppers. Preheat your broiler to high or heat a cast-iron skillet over high heat. Place the poblanos directly on the burner, under the broiler, or in the hot skillet. Turn them frequently with tongs until the skins are completely charred and blistered on all sides. This usually takes 5-10 minutes.
Step 2: Steam the chiles. Immediately transfer the hot, charred poblanos to a bowl and cover tightly with plastic wrap, or place them in a paper bag and seal it. Let them steam for 15-20 minutes.
Step 3: Peel and deseed the chiles. Once cooled enough to handle, gently peel off the charred skins. Make a slit lengthwise down one side of each chile, leaving the stem intact. Carefully remove the seeds and veins using a small spoon or your fingers. Pat the chiles dry thoroughly with paper towels.
Step 4: Prepare the cheese filling. Stuff each prepared poblano pepper generously with a stick of Oaxaca cheese. If desired, you can secure the opening with a toothpick.
Step 5: Make the egg batter. Separate the egg whites from the yolks. In a large, clean bowl, beat the egg whites with a pinch of salt using an electric mixer on high speed until stiff peaks form. In a separate small bowl, whisk the egg yolks lightly. Gently fold the egg yolks into the stiff egg whites until just combined.
Step 6: Dust the chiles. Lightly dust each cheese-stuffed chile with all-purpose flour. Shake off any excess flour.
Step 7: Heat the oil. Pour about 1-2 inches of vegetable oil into a deep, heavy-bottomed skillet or Dutch oven. Heat the oil over medium-high heat until it reaches 350-375°F (175-190°C).
Step 8: Batter and fry the chiles. Carefully dip each floured, stuffed chile into the egg batter, ensuring it’s completely coated. Gently lower the battered chile into the hot oil. Fry 1-2 chiles at a time for 2-4 minutes per side, until golden brown and crispy. Use a spoon to baste the top of the chile with hot oil as it fries.
Step 9: Drain and serve. Remove the fried chiles with a slotted spoon and place them on a wire rack set over paper towels to drain excess oil. Season lightly with a pinch of salt. Serve immediately with your favorite salsa or a simple tomato sauce.