In a large skillet, brown the ground beef over medium-high heat until no pink remains. Drain off any excess grease and transfer the browned beef to your slow cooker.
If desired, add the diced onion and minced garlic to the same skillet with a tablespoon of olive oil (not included in ingredients but recommended if sautéing). Sauté for 3-5 minutes until softened. Transfer the sautéed onion and garlic to the slow cooker with the beef. (Alternatively, you can add them directly to the slow cooker raw).
To the slow cooker, add the diced potatoes, sliced carrots, beef broth, Worcestershire sauce, dried mustard, salt, and black pepper. Stir all ingredients to combine thoroughly.
Cover the slow cooker and cook on low for 6-8 hours or on high for 3-4 hours, or until the potatoes and carrots are tender when pierced with a fork.
About 20-30 minutes before serving, in a small bowl, whisk together the milk and all-purpose flour until a smooth slurry forms with no lumps.
Add the softened cream cheese cubes and shredded cheddar cheese to the slow cooker. Pour in the milk-flour mixture. Stir well until all the cheeses are melted and the soup is creamy and slightly thickened. Continue stirring occasionally for about 15-20 minutes to ensure even melting and thickening.
Taste the soup and adjust seasonings (salt, pepper) if necessary. Serve hot, garnished with optional toppings like cooked bacon bits, chopped green onions, or dill pickle slices for that authentic cheeseburger experience.
Notes
For an even richer flavor, you can add a can of diced tomatoes (drained) along with the other vegetables. If you prefer a thinner soup, you can reduce the amount of flour or omit the milk-flour slurry entirely. This soup stores well in an airtight container in the refrigerator for up to 3-4 days. Reheat gently on the stovetop or in the microwave, adding a splash of milk or broth if it's too thick.