Brown the beef: In a large pot or Dutch oven, heat oil over medium-high.
Add ground beef and cook, breaking it up, until browned and no pink remains. Drain excess fat if needed. Season with a pinch of salt and pepper.
Sauté the aromatics: Add onion, carrots, and celery to the pot.
Cook 4–5 minutes, stirring, until softened. Stir in garlic and cook 30 seconds until fragrant.
Add potatoes and broth: Stir in potatoes, broth, salt, pepper, dried mustard (or Dijon), and Worcestershire. Bring to a boil, then reduce to a simmer.
Cook 10–15 minutes, until potatoes are tender.
Make the roux: In a small saucepan, melt butter over medium heat. Whisk in flour and cook 1–2 minutes, whisking constantly, until the mixture smells toasty and turns pale golden.
Thicken the soup: Slowly whisk milk into the roux until smooth. Simmer 2–3 minutes to thicken slightly, then pour this mixture into the soup pot.
Stir well and let it gently simmer 3–4 minutes more.
Finish with cream and cheese: Reduce heat to low. Stir in cream, then add shredded cheddar a handful at a time, stirring until fully melted and smooth. Do not boil after adding cheese.
Boost the burger vibe: Stir in ketchup and pickle brine if using.
Taste and adjust seasoning with more salt and pepper as needed.
Serve and garnish: Ladle into bowls and top with chives, bacon, and a few chopped pickles if you like. Crack some pepper on top and serve warm.