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