Preheat the broiler. Place the tomatoes and jalapeno cut-side down on a foil-lined broiler pan. Add the onion and garlic and broil until blackened, 7 to 10 minutes. Peel the garlic.
Meanwhile, heat about 1/2 inch vegetable oil in a deep saucepan over medium-high heat until a deep-fry thermometer registers 350 degrees F. Fry the tortillas in batches until light brown, about 1 minute. Remove with a slotted spoon and drain on paper towels; season lightly with salt while still hot.
Heat 1 tablespoon vegetable oil in a large skillet over medium-high heat. Add the sesame seeds and toast until golden, 2 to 3 minutes. Transfer to a blender along with the broiled vegetables, oregano, chile powder, 1 teaspoon salt and the cilantro stems. Puree until smooth.
Heat the remaining 1 tablespoon vegetable oil in the same skillet over high heat. Add the puree and cook, stirring often, until thickened, 8 to 10 minutes. (Partially cover the skillet if the sauce starts to splatter.) Reduce the heat to medium. Add the chicken and broth and heat through, 3 to 4 minutes. Fold in the tortillas and cook until softened, about 1 minute. Keep warm while you fry the eggs.
Divide the chilaquiles among plates. Top with the eggs, cheese, radishes and cilantro leaves. Drizzle with crema, if desired.
Photographs by Con Poulos
Recipe courtesy Food Network Magazine
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