Warm olive oil in a skillet over medium heat. Add onion and cook, stirring occasionally, until softened, 5 minutes. Add garlic and cook until fragrant, 1 minute more.
Scrape onions and garlic into a slow cooker. Add beans, pork chop, broth, 1 cup water and thyme and cook on low heat for 4 to 5 hours, until beans are tender, adding more water during cooking if necessary.
Discard thyme sprigs. Remove pork chop and shred meat. Return meat to soup. Season with salt and pepper, and then serve.