Mix cream cheese and cheddar cheese in a bowl. Evenly spoon the mixture into the pepper halves.
Place eggs, flour and bread crumbs in separate bowls. Dip the jalapenos into the egg, then flour, then back into the egg, then coat well with bread crumbs making sure they are all coated.
Heat the oil in a skillet on medium-high heat. Fry jalapeno peppers for 3 to 4 minutes or until golden brown.
Let drain on a paper towel-lined plate. Serve warm with ranch dipping sauce if desired.