In a large nonstick skillet cook sausage over medium heat about 5 minutes or just until browned. Remove from skillet. In the same skillet heat oil over medium-low heat. Add onion; cook about 5 minutes or until tender and just starting to brown, stirring occasionally.
Coat the bottom of a 3½- or 4-quart slow cooker with cooking spray or line the cooker with a disposable slow cooker liner. In the prepared cooker combine sausage, onion, potatoes, thyme and black pepper. Pour broth over mixture in cooker.
Cover and cook on low-heat setting for 5 to 6 hours or on high-heat setting for 2½ to 3 hours. Stir in sweet peppers. If desired, sprinkle with cheese.
If using low-heat setting, turn cooker to high-heat setting. Cover and cook for 15 minutes more. Before serving, sprinkle with tarragon. Use a slotted spoon for serving.