In a large bowl, add the pork, 1 1/2 tablespoons of kosher salt, black pepper, and coarse-ground mustard. Stir together until the meat is fully coated. Set aside.
Heat the olive oil in a large Dutch oven over medium-high heat. Add the onions and cook for 10 minutes, stirring occasionally.
Add the garlic and cook for 30 seconds until fragrant.
Add the seasoned pork and cook for 10 minutes, stirring occasionally until the meat has browned.
Add the fire-roasted diced tomatoes, canned black beans, canned dark red kidney beans, chipotle peppers in adobo sauce, red wine vinegar, fish sauce, the remaining 1/2 tablespoon of kosher salt, ancho chili powder, smoked paprika, ground cumin, ground cloves, ground cinnamon, and ground allspice. Stir together to combine.
Raise the heat to high and bring to a simmer. Reduce the heat to low, cover, and cook for 1 1/2 hours.
Stir and scrape up any bits that are stuck to the bottom of the Dutch oven.
Add the sweet potatoes, poblanos, and stir to combine. Cover and cook for 30 more minutes.
Serve in bowls topped with cilantro, sour cream, and avocado slices.