Coat the bottom inside of a slow cooker with olive oil. Lay zucchini slices and garlic slices onto olive oil layer; top with pork roast. Season roast with 1 tablespoon curry powder, salt, and pepper.
Pour tomatoes with green chile peppers into a large measuring cup; stir in bouillon cubes and boiling water until dissolved. Pour tomato-broth mixture into slow cooker. Spread minced garlic over top of roast.
Cook on Low until pork is tender, about 6 hours.
Transfer pork roast to a plate and shred into bite-size pieces using a fork. Return shredded pork to slow cooker; add white beans, garbanzo beans, rice, and remaining 2 tablespoons curry powder and stir.
