Fill a large pot with enough oil to reach a depth of 3 inches and heat until it registers 365 degrees on a deep-fry thermometer. In a shallow bowl, whisk together the flour and 1/2 teaspoon salt. In another shallow bowl, beat the eggs. Add the bread crumbs to a third shallow bowl.
Cut a slit down the length of each chile. Place a piece of cheese lengthwise at one long edge of each chile, then roll the chiles around the cheese. Working with one at a time, coat the stuffed chiles with the seasoned flour, then dip in the egg, letting the excess drip off, then coat with the bread crumbs, pressing the ends together to seal.
Working in batches, fry the chiles until browned, about 2 minutes, allowing the oil temperature to return to 365 degrees between batches. Transfer to paper towels to drain; season with salt.