Heat a heavy pot over medium-high heat (or heat a multicooker to 475). Season the pork chunks with salt and pepper, then add them to the pot to brown, approximately 5 minutes per side. Remove from the pot and add to a slow cooker.
Add the sliced onions to the pot and saute until they are golden brown and caramelized. Add a small amount of stock to the pot to deglaze the pan, scraping up the any browns bits on the bottom with a wooden spoon. Add the onions to the slow cooker.
Place 2 large sprigs of thyme on top of the pork and onions, then pour in the remaining stock. Cook on LOW for 6-7 hours, until the pork is tender and falling apart.
Shred the pork. Stir in the beans, corn, rice and sliced pepper, turn the slow cooker to HIGH, cover, and cook until the rice is tender, approximately 30-60 minutes.
Ladle soup into bowls. Squeeze a lime wedge over, then top with diced tomatoes, cheese, peppers and cilantro and serve.