Combine the grated cheddar cheese and cream cheese, divide into 16 equal portions, and roll into logs. Slit chiles along the side insert prepared logs into chiles, firmly wrapping chile around the cheese log.
At this point you can wrap the stuffed chiles in parchment paper, place in a gallon size freezer bag and freeze for later use. When using the freeze method there is no need to defrost the stuffed chiles prior to battering and frying.
Dredge the stuffed chiles into flour, and then batter place in hot shortening and fry until golden brown. Drain on absorbent towels.
Combine flour and salt in a medium-size mixing bowl, transfer to a serving platter. Beat egg whites until stiff, fold in the reserved yolks and 1 tablespoon of flour. Continue to the last step in the Chile Relleno recipe.