To make the braised pork: Preheat the oven to 350 degrees F.
Pat the pork dry of any juices and generously season with salt and pepper. Heat the vegetable oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Place the pork in the pot and brown well on all sides. Remove the pork and reduce heat to medium, add the onion, carrot, celery, fennel, garlic, thyme, bay leaves, salt, and pepper. Cook to soften the vegetables, about 10 minutes, then deglaze the pot with the wine, scraping up the bits stuck to the bottom of the pot. Add the chicken stock and stir, slide the pork back into the pot and bring liquids to low boil. Cover the pot and place in the oven for 2 to 2 1/2 hours, turning the meat 1/2 way through cooking. Keep the pork in the oven until the meat is tender and falls apart when pulled at with a fork.
Remove the pork from the pot, place on a platter, and when cool enough to handle, pull the meat apart with 2 forks, divide the meat and reserve one half. Strain the cooking liquids and add to the reserved pork.
To make the pickled onions and chiles: In a saucepan over medium-high heat, add the vinegar, water, sugar, 1 teaspoon salt, and coriander seeds, and bring to a boil, stirring until the sugar is dissolved. Arrange the onions and pepper rings in a small container with a tight-fitting lid and pour the brine over the top. Cool, cover, and store chilled for a minimum of several hours and up to several days. Cook's Note: The pickled onions and peppers make powerful companions to the smoky mild stew.
To make the red posole: Seed and stem the ancho chiles. Place the peppers in a pot and cover with stock, add a little water, if necessary, to cover. Reconstitute the peppers by bringing the liquids to a low boil, and then reduce the heat to simmer, and cook until the peppers are soft. Carefully transfer the peppers and their liquids to a food processor and process until smooth.
Meanwhile, heat about 2 tablespoons olive oil, a couple turns of the pan, in a skillet over medium heat, and add onions, garlic, and season with paprika, chile powder, cumin, salt, and pepper. Cook until the vegetables are very soft, 10 to 12 minutes, stir in the pepper puree, hominy, cilantro, 2 cups chicken stock, honey, the juice of 1 lime, and 1/2 the pulled pork. Add just enough water to form stew as loose or thick as you like, 1 to 2 cups additional liquid. Cool and store for a make-ahead meal.
To serve, heat the stew over medium heat. Once hot, spoon the stew into shallow bowls and top with pickled onions and jalapenos, queso fresco, and serve with warm charred tortillas for dipping and wrapping.