Place the sausage and onion in a large skillet over medium heat. Cook until the sausage is browned and the onion softens, breaking up the meat as it cooks.
Add the garlic and cook for one minute more, then transfer the mixture to the slow cooker.
Stir in the pumpkin puree, diced tomatoes, chicken broth, sage, thyme, salt, and pepper.
Cover and cook on low for 6 hours.
Stir in the kale, cover again, and cook for 30 more minutes until the kale wilts.