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1
Using a long-handled fork, char chiles over an open flame, turning, until skins are blackened, 4 to 6 minutes.
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2
(Alternatively, broil chiles on a broiler pan about 2 inches from heat, turning occasionally until skins are blistered and charred.)
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3
Transfer chiles to a bowl and let stand, covered, until cool enough to handle.
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4
Using a small knife, carefully scrape the charred skin off the chiles (leave the stems attached).
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5
Carefully cut a lengthwise slit in each chile to form a pocket, and cut out and discard the seeds.
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6
Stuff each chile with some of the mild cheddar, and thread shut with a toothpick.
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7
In a large saucepan, melt enough shortening to reach 1/2-inch up the sides, and heat to 375 degrees F. on a deep-fat thermometer.
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8
Preheat the broiler.
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9
In a bowl, combine flour, salt, and pepper.
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10
In another bowl, carefully fold yolks into egg whites.
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11
Working in batches, dredge the chiles in the flour and, using a slotted spoon, dip into the eggs to coat completely.
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12
Fry, turning occasionally, until golden, no more than a couple of minutes.
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13
Using a slotted spoon, transfer chiles (careful, they are delicate) to paper towels to drain.
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14
Arrange chiles on a flameproof plate and sprinkle with the sharp cheddar.
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15
Broil chiles just long enough to melt cheese and serve immediately, accompanied by salsa, if desired.
