Brown the beef: Heat oil in a skillet over medium-high. Add ground beef and cook until browned, breaking it into crumbles.
Season lightly with salt and pepper, then drain excess fat.
Sauté aromatics: In the same pan, add onion and cook 3–4 minutes until softened. Stir in garlic and cook 30 seconds until fragrant. Transfer everything to the slow cooker.
Load the crockpot: Add carrots, celery, potatoes, beef broth, tomato paste, Worcestershire, dried mustard, paprika, and a pinch of salt and pepper.
Stir to combine.
Slow cook: Cover and cook on Low for 6–7 hours or High for 3–4 hours, until potatoes are tender.
Make a quick roux: About 30 minutes before serving, melt butter in a small saucepan. Whisk in flour and cook 1 minute. Slowly whisk in the milk or half-and-half until smooth and slightly thickened.
Thicken the soup: Stir the roux into the crockpot.
Add cream cheese (if using) and whisk gently until melted and smooth.
Add the cheese: Sprinkle in the shredded cheddar a handful at a time, stirring until fully melted. Taste and adjust seasoning with more salt, pepper, and a splash of Worcestershire if needed.
Finish with “burger” touches: For that cheeseburger vibe, stir in a teaspoon of yellow mustard or top bowls with diced pickles. Ladle into bowls and add your favorite toppings.
Serve: Pair with toasted buns or crusty bread for dunking.
Enjoy hot.