Set an oven rack about 6 inches from the heat source and preheat the oven's broiler. Line a baking sheet with aluminum foil.
Place poblanos, cut-sides-down, onto the prepared baking sheet. Broil until skins blackened and blistered, about 5 minutes. Transfer poblanos to a bowl; tightly seal with plastic wrap. Allow peppers to steam as they cool, about 20 minutes. Remove and discard skins. Dice poblanos; set aside.
Cook bacon in a large pot over medium heat, stirring often, until fat renders and beginning to crisp, about 5 minutes. Drain on a paper towel-lined plate; discard all but 1 tablespoon drippings from the pot.
Increase heat to medium-high; add pork to the pot. Cook until browned on all sides, stirring occasionally, about 5 minutes. Transfer pork to a plate; reduce heat to medium. Add onion and garlic; cook and stir until onion has softened and is beginning to brown, about 5 minutes.
Add poblanos, jalapeños, cilantro, cumin, oregano, chile powder, salt, and cloves to the pot; cook for 1 minute. Add chicken stock, enchilada sauce, bacon, and pork; bring to a simmer over medium-high heat. Reduce heat to medium-low, cover, and simmer for 1 hour. Stir in hominy; cover the pot. Cook until pork is very tender, about 1 hour more.