Preheat broiler. Line a large rimmed baking sheet with aluminum foil and set aside.

Wash peppers and tomatoes. Place peppers on one half of foil-line baking sheet. Slice tomatoes in half, sprinkle with coarse salt and pepper, to taste. Place tomatoes, skin side up on other half of foil-lined baking sheet. 

Place baking sheet under broiler for 3 to 5 minutes at a time, watching carefully so as to not overcook. Tomatoes are done when skins begin to pucker. Remove tomatoes from baking sheet when done and place on a cutting board to cool. Continue roasting peppers on all sides until skins blacken and start to char. 

Once peppers are blackened on all sides, wrap them with a damp cloth or paper towels until cool enough to handle.

When tomatoes are cool enough to handle, remove skins. They should peel away easily. With a sharp knife, gently dice the tomatoes. Add additional salt and pepper, to taste and reheat in a saucepan until warm, if desired.

Separate the egg yolks from the egg whites. Place egg whites in a small bowl. Using a hand mixer, beat the egg yolks on high speed for 2 to 3 minutes until stiff peaks form. In a separate bowl, whisk the egg yolks until light and frothy. Set aside.

Once peppers have cooled, dry them well with a cloth or paper towels. Cut the tops off and carefully peel off their skins and remove the seeds. Stuff them with a mixture of cheddar and mozzarella cheese.

Place ½-inch of oil in a large skillet or cast iron pan. Heat on medium heat until a drop of water sizzles.

Gently fold in the egg yolks into the egg whites and stir just until incorporated, being careful not to overmix. This step is done best just before dipping peppers.

When oil is hot enough, gently dip peppers in egg mixture, coating well on all sides. Fry in oil about 3 to 4 minutes per side, until golden brown. When done, remove from oil and let drain on paper towels.

Serve chile rellenos with diced tomatoes, garnished with sour cream, avocado, and cilantro sprigs, if desired.