Special equipment: a deep-fry thermometer
To make the tomato sauce for serving, put the tomatoes in a blender. Add the chicken broth, garlic, onion and 1 teaspoon salt and blend until smooth, about 1 minute. Transfer the sauce to a medium saucepan and bring to a boil over medium-high heat. Boil until slightly reduced, about 5 minutes. Season the sauce with salt and pepper. Keep warm.
Carefully cut a lengthwise slit in each chile and scoop out the seeds. Stuff each with 2 to 3 strips of cheese (depending on the size of the chile), enclosing them tightly.
Place the flour on a baking sheet and season with salt and pepper. Dredge the chiles in the flour mixture, shaking off the excess.
In a large saucepan, heat the oil until a deep-fry thermometer registers 375 degrees F.
Using a hand-held mixer, beat the egg whites to soft peaks. Fold the beaten yolks into the egg whites, add 1/4 teaspoon salt and beat to stiff peaks.
Holding the chiles by the stem, dip them into the egg mixture to coat completely. Add to the oil and fry, turning occasionally, until golden brown all over, about 2 minutes per side. With a slotted spoon, transfer the chiles to paper towels to drain.
Place the chiles on each of 6 plates. Spoon the sauce equally over the chiles and serve.