Brown the beef: Heat a large, deep skillet over medium-high. Add the ground beef and cook, breaking it up, until browned with some crispy bits, 5–7 minutes.
Drain excess fat if needed, leaving about 1 tablespoon in the pan.
Soften aromatics: Add the diced onion and cook until translucent, 3–4 minutes. Stir in the garlic and cook 30 seconds until fragrant.
Build the base: Add tomato paste and cook, stirring, for 1 minute to caramelize slightly. Stir in ketchup, mustard, Worcestershire, smoked paprika, onion powder, salt, and pepper.
Add liquids and pasta: Pour in the broth, milk, and pickle brine (if using).
Stir to combine, then add the pasta. Bring to a gentle boil.
Simmer: Reduce heat to medium-low. Cover and cook, stirring occasionally to prevent sticking, until pasta is just tender, 10–12 minutes.
If the skillet looks dry before the pasta is done, add a splash of broth or water.
Finish with cheese: Turn off the heat. Stir in butter until melted. Add cheese a handful at a time, stirring until smooth and creamy.
Taste and adjust salt or mustard if needed.
Garnish and serve: Top with chopped dill pickles and sliced green onions for a true cheeseburger feel. Serve hot.