For Sauce: Char poblano peppers directly over a gas flame or under the broiler, rotating as needed to ensure the skin is blistered and charred on all sides. Use tongs to transfer roasted peppers to a bowl, then top with plastic wrap so the peppers steam. After 10 minutes, discard plastic wrap. Under cool running water, use clean hands to strip away the charred skin. Discard seeds.
Place a large skillet over medium-high heat; add tomatillos, jalapeño peppers, green bell pepper, onion, and garlic. Slightly toast, turning frequently, until the mixture is aromatic and just begins to deepen in color. Remove tomatillo mixture from the skillet.
Meanwhile, add pepitas to a small skillet over medium-high heat. Toast them lightly, tossing constantly with a spoon, until golden brown; remove from heat.
Add roasted peppers, tomato mixture, toasted pepitas, cilantro, salt, and water to the jar of a blender. Blend until smooth.
Heat oil for 1 minute in a large saucepan over medium heat, then pour in blended sauce. Cook sauce for 8 to 10 minutes, stirring constantly.
For Soup: Combine hominy, chicken, onion, garlic, bay leaves, marjoram, oregano, thyme, chicken bouillon, and water in a large stock pot. Bring to a boil over medium-high heat, then turn the heat to low and simmer until chicken is no longer pink at the center and juices run clear, 45 to 50 minutes. Skim off any foam or fat that rises to the surface during simmering. An instant-read thermometer inserted near the center of chicken should read 165 degrees F (74 degrees C).
Use tongs to remove the chicken to a plate; allow it to cool. Discard onion, garlic head, bay leaves, and thyme sprigs. Reserve the stock for the base of the soup.
When the chicken is cool enough to handle, use two forks to shred the meat. Set it aside.
As chicken cools, use a glass measuring cup to scoop out about 1/2 cup hominy and a bit of stock. Pour in a blender pitcher, and blend until smooth. Stir the mixture back into the pot with broth to thicken pozole.
Add tomatillo mixture to the soup. Cook for an additional 10 minutes to allow the flavors to combine. Try a taste; add more salt or chicken bouillon powder as needed, and add more water if you prefer a thinner pozole.
Turn off the heat, stir in shredded chicken.
To garnish: sprinkle soup with oregano and piquín pepper. Top with lettuce, onion, and radishes. Spread tostadas with Mexican crema to serve alongside.
Cook’s Note
In Mexico, it is traditional to eat pozole with tostadas spread with Mexican crema, but this is optional, Jennifer says.