Preheat the oven's broiler and set the oven rack 6 inches below the broiler.
Line a baking sheet with aluminum foil.
Place peppers on the prepared baking sheet and cook under preheated broiler, turning occasionally until all the skin is blistered and blackened.
Remove the blackened peppers into a bowl and cover with plastic wrap and allow peppers to cool.
Rinsed the cooled peppers under cold water to peel of the skin. Cut a slit along the long side of each pepper to remove the seeds and core. Pat dry with paper towels.
Whisk the egg yolks in a bowl with the baking powder. In a second bowl, beat the egg whites with an electric mixer until the whites form stiff peaks. Gently fold the egg whites into the yolk mixture.
Place flour into a shallow bowl.
Cut cheese into 3/4 inch strips. Stuff the peppers with strips of cheese.
Heat the vegetable oil in a skillet over medium heat.
Roll each stuffed pepper in flour, shaking off excess flour and dip the peppers into the egg mixture to coat both sides.
Gently lay the coated peppers into the hot oil. Fry peppers until lightly golden brown and the cheese has melted, about 5 minutes on each side.
Allow to cool slightly before serving.