Step 1Heat the oven to 350 degrees.
Step 2Wash and dry the chiles. Place them in a baking pan and drizzle them with a little oil. Roast them 20 minutes, turning them over after 10 minutes. Remove them from the oven and let them cool completely. Carefully remove the peel from each chile, leaving the stem ends intact. Gently cut a small slit at the top of each chile and carefully cut off the seed cluster. Place a piece of cheese inside each. Place 1/4 cup of flour on a dinner plate. Dredge each side of each chile until completely covered, adding more flour to the plate as needed.
Step 3Beat the egg whites until stiff. Add 1 1/2 tablespoons of flour to the whites and beat. Add the yolks all at once and blend until well mixed.
Step 4Heat 2 cups of oil in a heavy skillet until very hot. Submerge the chiles in the egg batter, holding them by the stems, 1 at a time. When they're completely coated, place 2 to 3 chiles at a time into the hot oil; do not crowd them. When golden brown on the bottom, 3 to 4 minutes, turn the chiles over and cook the other side until golden brown. Drain them on paper towels. Serve the rellenos plain or with a sauce.