Place whole peppers on a foil-lined baking sheet. Bake in a 425 degree F oven for 20 to 25 minutes or until skin is bubbly and browned. Wrap peppers in the foil; seal and let stand for 20 to 30 minutes or till they are cool enough to handle. Make a slit in each pepper from the top to the bottom. Remove seeds.
Fill peppers with cheese. Secure peppers with wooden toothpicks, if needed. Coat the outside of the peppers with some of the flour.
Whisk eggs in a bowl. Dip peppers into the beaten eggs. Coat evenly with the remaining flour.
In a heavy skillet, heat the cooking oil to 365 degree F. Fry peppers, a few at a time, for 3 to 4 minutes or till golden, turning once. Drain on paper towels and serve warm with salsa and sour cream, if you like. Makes 6 servings.