Bring a large pot of water to a rolling boil and season generously with salt; add the spaghetti and cook until al dente according to package directions (usually 8–10 minutes). Reserve 1 cup of the pasta cooking water, then drain the pasta and set aside.

While the pasta cooks, heat a large heavy skillet over medium-high heat and add the olive oil. Once shimmering, add the ground beef and season with a pinch of salt and black pepper. Cook, breaking up the meat with a wooden spoon, until fully browned and no longer pink, about 6–8 minutes; transfer browned meat to a bowl and set aside, leaving fat in the skillet.

Reduce the skillet heat to medium, add the butter and let it melt. Add the minced garlic and sauté until fragrant and lightly golden, about 30–45 seconds, stirring constantly to avoid burning.

Pour in the heavy cream and beef broth, stirring to combine with the garlic and butter. Scrape browned bits from the bottom of the pan with a wooden spoon to incorporate flavor. Bring the liquid to a gentle simmer and let it reduce slightly for 3–5 minutes.

Stir the grated Parmesan into the simmering cream mixture until melted and smooth. Season the sauce with Italian seasoning, paprika, and additional salt and black pepper to taste. Continue to simmer on low for another 2 minutes to allow flavors to meld.

Add the drained spaghetti to the skillet and gently toss to coat the noodles in the garlic cream sauce. If the sauce feels too thick, add a few tablespoons of the reserved pasta cooking water at a time until you reach a glossy, clingy consistency that coats the noodles.

Fold in one cup of the shredded mozzarella so it melts into the sauce, leaving the remaining cup for topping. Taste and adjust seasoning, adding more salt or black pepper as desired.

Return the browned ground beef to the skillet, mounding it over the center of the sauced spaghetti. Sprinkle the remaining shredded mozzarella and a light dusting of paprika over the meat and cheese. Cover the skillet for 1–2 minutes off heat just to let the residual heat melt the top layer of cheese.

Serve immediately in shallow bowls, finishing each portion with a generous sprinkle of chopped fresh parsley and an extra grind of black pepper.