Chiles Rellenos Divorciados

In a small, dry skillet over medium heat, toast sesame seeds until fragrant and golden, 2 to 3 minutes.

Place poblanos directly on the grates of a gas stove and char over high heat, turning a few times, until blackened all over, 6 to 8 minutes. Transfer to a bowl and cover; let steam 15 minutes.

Meanwhile, preheat oven to broil with a rack in position closest to heating element. Arrange tomatoes (cut-sides up), onion, garlic, jalapenos, and half of tomatillos in a single layer on a rimmed baking sheet. Broil, turning onion, garlic, jalapenos, and tomatillos once halfway through, until blackened in places and beginning to soften, 10 to 15 minutes. Transfer tomatoes, half of onion and garlic, and 1 jalapeno to a blender; add 1/3 cup broth, 1 tablespoon lime juice, and 3/4 teaspoon salt and puree until smooth. Transfer mixture to a bowl; rinse out blender jar. Place charred and raw tomatillos in blender with cilantro, 3/4 teaspoon salt, and remaining onion, garlic, jalapeno, 1/3 cup broth, and 1 tablespoon lime juice. Puree until smooth. Transfer to another bowl.

Place poblanos on a work surface; gently rub with a paper towel to remove skins, taking care not to tear flesh. Holding the tip of a knife at stem end of a pepper, make a lengthwise slit about 1 1/2 inches long; carefully remove seeds. Repeat with remaining poblanos. Holding slits open with one hand, stuff peppers with cheese, dividing evenly.

Heat 1 inch of oil in a large, heavy skillet, preferably cast iron, over medium-high until a deep-fry thermometer reads 375 degrees. (Lower heat to regulate temperature, if necessary.) In a bowl, whisk egg whites to stiff but not dry peaks. In another bowl, whisk egg yolks with flour and 1 teaspoon salt until thickened slightly and pale. Whisk 1/3 of egg whites into yolk mixture until smooth. Gently fold in remaining egg whites, leaving some streaks (do not overmix). Fill the bottom of a pie plate with flour.

Dredge 3 poblanos in flour, turning to evenly coat. Lift 1 poblano and cradle it in your hand, patting with the other to remove excess flour, then hold stem end with one hand and tip end with other hand, slit-side up. Lower into egg batter to fully submerge, then lift again, allowing any excess batter to fall back into bowl. Carefully lower into skillet. Quickly dip remaining 2 floured poblanos in egg mixture and transfer to skillet. Fry, flipping once halfway through, until puffed and golden brown, 5 to 7 minutes. Transfer with a slotted spoon to a rimmed baking sheet lined with a wire rack. Repeat with remaining 3 poblanos.

To serve, spread 1/4 cup charred-tomato salsa on one side of each plate, and 1/4 cup tomatillo salsa on other side. Top with a fried poblano, sprinkle with cilantro and sesame seeds, and serve immediately.