Broil the Hatch chiles on high for 5–10 minutes per side until blistered and charred. Steam in a sealed bag for 10–15 minutes.

Carefully peel the skins off, slice a slit to remove seeds, and stuff each chile with Oaxaca cheese, securing with toothpicks.

Beat egg whites until stiff peaks form, then gently fold in egg yolks.

Whisk together flour, salt, and garlic powder in a shallow dish.

Heat oil in a deep skillet to 350°F (175°C) and dredge stuffed chiles in flour mixture and batter before frying for 2–3 minutes on each side.

Blend tomatoes, onion, garlic, cilantro, and salt until smooth. Heat sauce in a saucepan until boiling, then simmer for 10-15 minutes.

Plate the fried chiles and ladle warm sauce over them, garnishing with salsa verde or Mexican crema if desired.