In a large heavy-bottomed pot, warm the bacon fat or olive oil over medium-high heat until shimmering. Add the poblano and jalapeño peppers along with the white parts of the scallions, pepitas, garlic, cumin seeds, coriander seeds, allspice berries, and a generous pinch of kosher salt. Stir and sauté until the vegetables begin to soften and release their aroma, about 5 minutes.

Add the tomatillos and continue cooking, stirring occasionally, until they become tender and start to brown slightly around the edges, about 5 to 6 minutes. This light caramelization deepens the flavor of the broth.

Remove the pot from the heat. Working in batches, transfer portions of the cooked vegetable mixture to a blender, adding some of the chicken broth each time to help it blend smoothly. Puree until velvety and then pour into a large mixing bowl. Repeat until all the vegetables and broth are blended. Return the pureed mixture to the pot and stir in the drained hominy.

Set the pot back on the stove over high heat and bring the mixture to a boil. Once boiling, reduce the heat to medium-low, cover, and let it simmer gently for about 30 minutes to allow the flavors to meld and the broth to thicken slightly.

Meanwhile, combine the cilantro, scallion greens, and 2 cups of water in the blender. Puree until completely smooth and vibrant green. Add this cilantro puree along with the shredded chicken to the simmering soup. Remove the pot from the heat and stir gently to incorporate everything. Let it rest for several minutes so the chicken warms through and absorbs the flavors.

Ladle the pozole into bowls and serve hot, topped with sliced onion, radishes, avocado, crushed chicharrones, and a sprinkle of fresh oregano. Offer lime wedges on the side for a bright citrus finish. This hearty Mexican stew is best enjoyed freshly served, bursting with layers of smoky, tangy, and herbal flavor.