Heat butter in a soup pot or Dutch oven with a heavy bottom over medium-high heat, then add the ground beef. Spread out with downward slices of a spatula until it covers the bottom of the pot, then season with liquid smoke, seasoning salt, and black pepper. Be patient and don't turn or stir the meat until the first side has begun to brown. When you do turn it over, take care not to break it into tiny crumbs; you want some larger chunks to keep a burger vibe going!
Taste and adjust if more salt is needed; sprinkle Kitchen Bouquet, if using, across the surface of the meat and toss until fully combined.
Add onion and garlic; cook and stir with the beef until the aromatics are softened.
Reduce heat to medium; stir in tomato paste. Cook and stir until the paste darkens and starts to smell toasty, but be careful not to burn it!
Add the beef broth, mustard, and pickle juice. Stir well and simmer 10 minutes.
Lower heat to medium-low; stir in milk or half-and-half. Cook for 2 minutes, stirring constantly.
Remove from heat. Stir in Velveeta cubes until melted; add the cheddar and stir again until well combined and melty.
Serve hot with a mountain of crispy fries (and other garnishes) on top.