Roast the peppers: Roast poblanos over a gas flame, on a grill, or under a broiler, turning every couple of minutes, until the skins are blistered and blackened all over (about 8–10 minutes).
Steam & peel: Transfer peppers to a bowl and cover, or place in a plastic bag. Let steam for 10 minutes, then gently rub/peel off the charred skins. Pat the peppers dry.
Seed: Make a slit down one side of each pepper. Carefully remove seeds and membranes, keeping the stem on if possible and trying not to tear the pepper.
Stuff: Fill each pepper with a generous amount of cheese (about 2 oz per pepper), then press the sides together to enclose the filling.
Make the egg batter: Beat egg whites to stiff peaks. Gently beat in yolks, then fold in 1/4 cup flour, baking powder, and salt just until combined (keep the batter airy).
Heat the oil: Pour oil into a deep skillet to a depth of about 2 inches. Heat to 375°F (190°C).
Coat: Lightly dust each stuffed pepper with flour (this helps the batter stick). Dip into the egg batter, coating all over.
Fry: Carefully lower peppers into the hot oil. Fry 2–3 minutes per side, turning gently, until deep golden. Work in batches to avoid crowding and to keep oil temperature steady.
Drain & serve: Transfer to paper towels to drain. Serve immediately, topped with crumbled queso fresco if desired, and salsa roja or salsa verde on the side.