Warm the pot: Set a large, heavy-bottomed pot or deep skillet over medium heat. Add olive oil or butter and let it heat until shimmering.
Brown the beef: Add ground beef and break it up with a spoon.
Cook until no longer pink, about 5–7 minutes. If there’s excess grease, drain it, leaving about 1 tablespoon in the pot.
Sauté aromatics: Add the chopped onion and cook until soft and translucent, 3–4 minutes. Stir in the minced garlic and cook 30 seconds, just until fragrant.
Season and build flavor: Stir in salt, pepper, and smoked paprika.
Add ketchup, mustard, and tomato paste. Mix well so the beef is coated and the paste darkens slightly, about 1 minute.
Add liquids and pasta: Pour in broth and milk. Scrape up any browned bits from the bottom.
Bring to a gentle boil, then add the pasta.
Simmer: Reduce heat to a strong simmer. Cook uncovered, stirring every couple of minutes so the pasta doesn’t stick, until al dente and most of the liquid is absorbed, about 10–12 minutes. If it looks dry before the pasta is tender, add a splash of broth or water.
Make it cheesy: Lower the heat.
Stir in cheddar, mozzarella, and cream cheese (if using) until smooth and melted. The sauce should be glossy and cling to the pasta.
Add the “burger” touch: Fold in chopped dill pickles or relish. Taste and adjust seasoning with more salt, pepper, or a pinch of red pepper flakes.
Garnish and serve: Top with sliced green onions and extra pickles if you like.
Serve hot, right out of the pot.