In a medium skillet over medium-high heat, cook ground beef or turkey and onion until meat is browned. Add garlic and cook for an additional minute. Place in the slow cooker.
Add potatoes, carrots, chicken broth, and salt to the slow cooker and cook on low for 8 hours or high for 4 hours.
In a medium bowl, whisk together milk and flour. Stir flour mixture and spinach into the slow cooker, cover, and cook for an additional 30 minutes until soup has thickened slightly. Stir in the shredded cheese and serve.
