In a large skillet over medium heat, cook the ground beef until browned and cooked through, breaking it up with a spoon as it cooks. Drain excess fat.
Add the diced onion and minced garlic to the skillet with the beef. Cook for 3-4 minutes until the onion is softened. Remove from heat.
In the slow cooker, combine the cooked beef mixture, beef broth, diced potatoes, carrots, celery, salt, black pepper, smoked paprika, and dried thyme. Stir to combine.
Cover and cook on low for 6 hours, or until the vegetables are tender.
About 30 minutes before serving, whisk together the all-purpose flour, whole milk, and heavy cream in a bowl until smooth.
Slowly stir the milk mixture into the slow cooker. Cover and cook on high for 30 minutes, stirring occasionally, until the soup thickens.
Add the shredded cheddar cheese to the slow cooker and stir until melted and fully incorporated.
Taste and adjust seasoning with additional salt and pepper if desired.
Ladle the soup into bowls and serve warm.