Preheat the broiler. On a large, rimmed baking sheet, combine the first 5 ingredients in a single layer; season with salt and pepper. Broil, turning once, until the vegetables are tender and charred in spots, about 15 minutes. Peel the garlic cloves, then transfer the garlic and the charred vegetables with any juices to a blender or a food processor. Add 1 cup cilantro; pulse until the salsa verde is coarsely pureed.
In a large, heavy pot, heat the oil over medium-high. Season the pork. Working in batches, cook the pork, turning occasionally, until browned, 5 to 6 minutes per batch. Using a slotted spoon, transfer to a plate.
Return the pork to the pot. Add the oregano and cumin and stir 1 minute. Add the salsa verde; bring to a boil. Reduce the heat to low, then cover and simmer, stirring occasionally, until the pork is almost tender, 1 to 11/2 hours. Add the squash and hominy; cover and simmer until the squash is tender, 20 to 30 minutes. Season. Let cool slightly, then refrigerate uncovered until cold, 2 to 3 hours. Transfer to a freezer-safe container; freeze up to 2 months.
Transfer the stew to a pot. Cover and rewarm, stirring occasionally, over medium-low, until the stew is heated through, about 15 minutes. Divide among bowls and top with cilantro leaves.