Trim any excess fat off of the pork shoulder and cut it into 2" pieces. Place the meat into a large Dutch oven with a lid. Add the lime juice, garlic, chili powder, coriander, cumin, and salt. Add water to cover the pork (level to the top of the meat). Bring the mixture to a boil, then cover and reduce to medium-low, cook for 30 minutes.
Remove the lid and continue cooking on medium (or a simmer) for 1 hour and 45 minutes; the liquid should have reduced substantially by now.
Add the onions and minced jalapeños, and cook until tender. Pour in the water and the chicken broth, salsa, and beans, bring the mixture up to a boil. Once the mixture is boiling, add the rice, and cook until tender.
Serve with wedges of lime and garnish with cilantro.
Notes
Try adding fresh Hatch chiles for even more flavor!STORE any Chili Verde Soup leftovers in an airtight container in the refrigerator for up to 3-5 days. You can also FREEZE the dish for up to 3 months.To REHEAT, thaw in the fridge overnight if frozen, then warm on the stovetop over medium heat until hot, adding a splash of broth if needed. Alternatively, microwave in a microwave-safe dish, stirring occasionally, until heated through.