Heat the olive oil in a large skillet over medium heat. Add the sausage links and cook until browned on all sides, about 5 minutes. Transfer the sausages to the slow cooker.
Add the diced onion and minced garlic to the same skillet. Cook for 2 minutes until the onion softens, then scrape everything into the slow cooker.
Add the drained cannellini beans, diced tomatoes, chicken broth, dried thyme, and dried oregano to the slow cooker. Stir gently to combine.
Season with salt and black pepper. Cover and cook on low for 6 hours or on high for 3 hours.
Slice the sausages into thick pieces and return them to the slow cooker. Stir to mix everything together.
Serve hot, topped with chopped fresh parsley and grated Parmesan cheese.