In a large skillet over medium heat, cook the ground beef until browned and no longer pink, about 7-10 minutes. Drain excess fat and transfer the beef to a 6-quart crockpot.
Add the finely chopped onion, minced garlic, chicken broth, and diced potatoes to the crockpot. Stir to combine. Cover and cook on low for 6 hours or high for 3 hours, until the potatoes are tender.
In a medium saucepan over medium heat, melt the butter. Whisk in the flour and cook for 1-2 minutes, stirring constantly, until golden and bubbly. Slowly whisk in the milk, ensuring no lumps remain, and cook for 3-4 minutes until thickened.
Pour the milk mixture into the crockpot and stir to combine. Add the kosher salt, black pepper, dried parsley, and dried thyme. Stir again.
Cover and cook on high for an additional 30 minutes, until the soup is hot and slightly thickened. Stir in the shredded cheddar cheese and sour cream until fully melted and smooth.
Ladle the soup into bowls and garnish with toasted hamburger bun strips if desired. Serve hot.