Bring a large pot of water to a boil and add 1 tbsp salt. Cook the spaghetti 1 minute short of the package time so it stays slightly firm. Reserve 1 cup of the pasta water, drain, and do not rinse.
While the pasta cooks, heat a large, deep skillet over medium-high heat. Add the ground beef in one layer and press it flat. Leave it undisturbed for 3 to 4 minutes so it builds a dark, caramelized crust.
Break the beef into crumbles and season with 1 tbsp Cajun seasoning, 1 tsp smoked paprika, the garlic powder, onion powder, ½ tsp salt, and the black pepper. Cook 5 to 6 more minutes, until deeply browned with dark crispy edges.
Spoon off all but 1 tbsp of the fat. Push the beef to one side, add 2 tbsp butter and the garlic, and stir the garlic in the butter for 30 to 45 seconds, until fragrant but not browned. Stir it into the beef, then transfer everything to a bowl.
Reduce the heat to medium and add the remaining 2 tbsp butter to the same pan. Stir in the remaining 1 tbsp Cajun seasoning, the remaining 1 tsp smoked paprika, and 1 tsp Italian seasoning. Let the spices bloom for 30 seconds so the butter turns reddish-orange.
Pour in the beef broth and scrape up all the browned bits from the bottom of the pan. Simmer 1 minute.
Reduce the heat to medium-low and pour in the heavy cream. Simmer gently for 3 to 4 minutes, stirring often, until it thickens slightly and coats the back of a spoon. Do not let it boil hard.
Add the cream cheese cubes and whisk for 2 minutes, until completely melted and smooth.
Take the pan off the heat and let the bubbling stop for 1 minute. Whisk in ¾ cup Parmesan, ¾ cup cheddar, and 1 cup mozzarella a handful at a time, waiting until each addition melts before adding the next. The sauce should be thick, velvety, and pale orange.
Return the pan to low heat. Add the spaghetti and the beef, and toss with tongs until every strand is coated. Loosen with the reserved pasta water, a splash at a time, until the sauce turns glossy and clings to the pasta. It will thicken as it sits.
Sprinkle the remaining ½ cup mozzarella, ¼ cup cheddar, and ¼ cup Parmesan over the top. Cover and cook on low for 1 to 2 minutes, until the cheese melts into gooey, stretchy patches.
Finish with the remaining ½ tsp Italian seasoning and a light dusting of Cajun seasoning and smoked paprika. Rest 2 minutes, then serve immediately in large bowls, piled high, with the creamy sauce pooling at the base.