Place shredded potatoes, carrots, onion, celery, and garlic in a 4-qt slow cooker. Pour chicken broth over top. Cook on high heat 3-4 hours OR on low 5-6 hours until vegetables are tender and softened.
In a medium skillet over medium-high heat, brown beef until no longer pink. Stir into crockpot mixture and set aside.
Wipe same skillet clean and melt butter over medium-high heat. Whisk in flour, then slowly whisk in milk until mixture is smooth. Bring to a simmer over medium-high heat, stirring occasionally until mixture is thickened. Remove from heat and whisk in cheese, parsley, and salt and pepper to taste.
Add creamy sauce mixture to crockpot and stir to combine. Season soup with salt and pepper to taste. Let soup cook on high heat in crockpot an additional 30-60 minutes until heated through and soup is thick and creamy. Enjoy soup hot!