4 large fresh poblano peppers
2 1/2 cups Jack cheese, coarsely grated
For sauce
1 1/2 pounds Heirloom tomatoes, coarsely chopped
1 cup water
1/4 cup chopped white onion
2 large garlic cloves
1 tablespoon distilled white vinegar
1 teaspoon sugar
1 teaspoon dried oregano (preferably Mexican)
2 tablespoons corn oil or other vegetable oil
Frying ingredients
2 to 3 cups corn oil or other vegetable oil
4 large eggs, separated
1/4 cup all-purpose flour
Roast chiles:
Roast chiles on their sides on racks of gas burners (1 or 2 per burner) over medium-high heat, turning with tongs, until skins are blistered and slightly charred, 4 to 6 minutes. (Or broil on rack of a broiler pan about 2 inches from heat.) Immediately transfer to a large bowl and cover, then let stand 20 minutes.
Make tomato sauce while chiles stand:
Purée all sauce ingredients except oil with 11/4 teaspoons salt in a blender until smooth, then strain through a medium-mesh sieve into a bowl, pressing on solids, then discarding them. Heat oil in a deep 12-inch heavy skillet or heatproof casserole (preferably one that can go to the table) over medium-high heat until it shimmers. Carefully pour in sauce and simmer gently, stirring occasionally, 10 minutes (sauce should still be thin). Season with salt.
Stuff and fry chiles:
Carefully rub off skins from chiles, leaving stems attached. Cut a slit lengthwise in each chile with kitchen shears, then carefully cut out seedpod (including attached ribs) without tearing chile (hotter chiles smell stronger when cut). Wipe chiles clean with a paper towel if necessary.
Stuff chiles with cheese and enclose filling by overlapping slit slightly if possible, then transfer to a plate. (Use a toothpick to mark any hotter chiles if desired.)
Heat 1/2 inch oil in another 12-inch heavy skillet over medium heat until it registers 360°F on thermometer.
While oil heats, beat egg whites with 1/8 teaspoon salt using an electric mixer until they just hold stiff peaks. Whisk yolks with 1/8 teaspoon salt in a large bowl, then gently fold in whites.
Put flour in a fine-mesh sieve and dust chiles, turning them to lightly coat all sides.
When oil is ready, dip chiles, 1 at a time (hold chile by stem), in egg coating, spooning it over chile to cover completely, then fry, turning once, until golden on all sides (lap oil over any lighter areas), 4 to 5 minutes. Transfer chiles with a slotted spoon to paper towels to drain.
Meanwhile, reheat sauce over low heat. Lay chiles in sauce to serve.
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