Cook sausage in a nonstick skillet over medium-high heat; stir frequently and break up meat with a spatula into lima bean-sized pieces, until browned, about 5 minutes. Use a slotted spoon to remove sausage from skillet; add to a 6-quart slow cooker.
Add chopped onion and celery to the same skillet; cook and stir until vegetables begin to soften, 3 to 5 minutes. Add minced garlic and cook, stirring, about 30 seconds.
Pour vegetable mixture into the slow cooker. Add tomatoes with juices; break tomatoes into bite-sized pieces. Add chicken stock or broth, stir to distribute evenly, cover, and cook on Low 7 or 8 hours, or on High 3 to 4 hours.
About halfway through the cooking process, season with salt and pepper, and add Italian herb seasoning blend. See note.
About 30 minutes before serving, turn slow cooker to High, add tortellini and kale, and adjust seasoning. Cover and cook until tortellini is tender, about 30 minutes.
Serve warm, and garnish with grated Parmesan cheese.