Preheat a gas burner or broiler. Place the poblano peppers directly over the flame or under the broiler, turning with tongs until the skin is evenly charred and blistered on all sides, about 8–12 minutes. Transfer peppers to a heatproof bowl and cover tightly with plastic wrap or a plate for 10–15 minutes to steam (this loosens the skin).

Once cool enough to handle, peel off the charred skin using your fingers or a towel; avoid rinsing under water (rinsing removes flavor). Make a lengthwise slit down one side of each pepper and gently remove seeds and membranes with a small spoon, keeping the stem intact if possible. Be careful not to tear the pepper; leave enough flesh to hold filling.

If you prefer smaller peppers or easier stuffing, make a small slit at the top and remove seeds through the opening. Pat peppers dry with paper towels and set aside.

Prepare filling

Heat 1 tablespoon vegetable oil in a skillet over medium heat. Add the finely chopped onion and sauté until translucent, about 4–5 minutes. Add minced garlic and cook 30 seconds until fragrant. If using shredded chicken, add it now and stir to warm through. Season the mixture with 1 tsp salt and 1 tsp black pepper. Remove from heat and let cool slightly.

Stuff each pepper: place a 3/4" cheese stick (or a small handful of shredded cheese or combined cheese + a little chicken filling) into each pepper cavity. Don’t overfill; leave room so you can close the pepper without ripping. If needed, secure the slit with kitchen toothpicks to hold the pepper closed while battering and frying.

Batter & Frying

Prepare dredge and batter

Place the 1 cup flour in a shallow dish and season lightly (optional: 1/4 tsp salt). Separate the eggs into two medium bowls: yolks in one bowl, whites in another. Whisk the yolks until smooth. In the bowl with egg whites, add 1 tsp salt and 1 tsp baking powder. Using an electric mixer (or a whisk and elbow grease), beat the egg whites to stiff peaks. The mixture should hold a peak when you lift the beaters. If the whites are too stiff or dry, add up to 2 tablespoons cold water or club soda to loosen slightly.

Fold the beaten egg whites gently into the yolks in two additions, using a spatula and a lifting motion so you keep as much volume as possible. You want a fluffy, thick batter that will coat the peppers.

Dredge and coat peppers

Heat 1–2 inches of vegetable oil in a large, heavy skillet over medium-high heat to 350°F (175°C) if using a thermometer. Pat the stuffed peppers dry again. Lightly dredge each pepper in the flour, shaking off excess (the flour helps the batter adhere). Immediately dip the floured pepper into the egg batter, turning to coat completely and gently lifting out so excess batter runs off.

Fry the chiles

Carefully lower the battered pepper into the hot oil using tongs. Do not overcrowd the pan; fry in batches (2–3 at a time depending on pan size). Fry until golden brown and puffed, turning once carefully, about 3–4 minutes per side. Adjust heat as needed so oil stays around 325–350°F and the batter cooks through without burning (lower heat slightly if browning too quickly).

Transfer fried chiles to a wire rack or paper towel-lined plate to drain. If you used toothpicks, remove them after frying (be careful, they will be hot). Keep warm in a low oven (200°F / 95°C) while you finish frying remaining peppers.

Sauce (optional) & Finish

Make a simple roasted tomato sauce

While chiles are frying (or beforehand), roast the tomatoes and quartered onion: place tomatoes and quartered onion on a baking sheet under the broiler or on a hot skillet until blistered and softened, about 8–12 minutes, turning once. Alternatively, char tomatoes in a skillet. Allow to cool slightly.

Place the roasted tomatoes, onion, and 2 garlic cloves in a blender with 1 teaspoon oil, 1 teaspoon salt, and 1 teaspoon sugar (optional). Pulse until smooth or leave slightly chunky according to preference. Taste and adjust salt. If the sauce is very thick, add 1–2 tablespoons water to reach desired consistency. Heat the sauce briefly in a small saucepan to meld flavors if desired.

To serve: spoon a small pool of warm tomato sauce onto each plate (or serve sauce on the side). Place 1–2 fried chiles on the sauce. Drizzle or dollop crema or sour cream over the chiles, sprinkle chopped cilantro, and serve with lime wedges.

Optional: serve with warm corn tortillas, rice, or refried beans to complete the meal.