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Heat the broiler with a rack about 6 inches from the element. Place the poblanos on a rimmed baking sheet and broil until charred, about 10 minutes. Flip the chilies and broil until charred on the second sides, 3 to 5 minutes. Transfer to a medium bowl, cover and let steam to loosen the skins while you make the puree and cook the chicken. Turn the oven to 375°F.
In a blender, combine the tomatillos, garlic, vinegar, 1 cup of cilantro, 2 teaspoons of cumin and 1 teaspoons salt. Blend until smooth, about 1 minute, scraping the blender jar as needed; set the puree aside.
In a large Dutch oven over medium-high, heat the oil until shimmering. Carefully add the puree (it may splatter) and cook, stirring occasionally, until slightly reduced and a spoon drawn through leaves a brief trail, about 6 minutes. Remove ½ cup of the sauce and set aside. To the remaining sauce in the pot, add the chicken, onion, the remaining 1 teaspoon cumin, 1/4 teaspoon salt, and ½ teaspoon pepper. Bring to a simmer, then cover, reduce to medium-low and cook, stirring occasionally, until a skewer inserted into the chicken meets no resistance, 15 to 20 minutes.
While the chicken cooks, peel the skins off the chilies and remove and discard the stems and seeds. Chop the chilies and set aside. When the chicken is done, remove the pot from the heat. Using 2 forks, shred the chicken; you should have about 3½ cups chicken in salsa verde. If you have more, return the pot to medium heat and cook, stirring occasionally, until reduced. Stir in the corn, the ¼ cup of the chopped cilantro and the chopped chilies. Taste and season with salt and pepper.
Wrap the exterior of a 9-inch springform pan with a sheet of foil and set on a rimmed baking sheet. Add half of the reserved salsa to the pan and spread in an even layer. Line the bottom of the pan with 2⅔ tortillas, tearing them as needed to fit; it’s fine if the tortillas overlap slightly and if a few small spots are uncovered. Spoon in half of the chicken mixture and distribute in an even layer. Dollop with half of the crema, then spread evenly. Sprinkle with a third of the pepper Jack cheese. Repeat the layering using another 2⅔ tortillas, the remaining chicken mixture, the remaining crema and half of the remaining pepper Jack. Layer in the remaining tortillas, then spread evenly with the remaining reserved salsa. Sprinkle on the remaining pepper Jack followed by the cotija. Bake the pastel on the baking sheet until browned on top and bubbling at the edges, about 35 minutes.
Set the baking sheet on a wire rack. Sprinkle the pastel with the remaining ¼ cup chopped cilantro and the pumpkin seeds (if using). Let rest for at least 30 minutes or up to 1 hour.
To serve, run a knife around the inside of the springform pan to loosen. Remove the foil, set the pan on a large, flat platter and remove the sides. Cut into wedges and serve.