Dice the onion into 1/4-inch pieces and mince the garlic cloves. Season the ground beef generously with salt and pepper. Heat a large pot or Dutch oven over medium-high heat and add the seasoned beef, breaking it apart as it cooks. Once the beef is browned (about 5-7 minutes), add the diced onion and cook until softened, about 3-4 minutes. Drain any excess fat if needed, then stir in the minced garlic and cook for 1 minute until fragrant.
Add the Worcestershire sauce and tomato paste to the browned beef mixture, stirring well to coat everything evenly. Cook for 1-2 minutes to let the tomato paste caramelize slightly and the Worcestershire sauce integrate into the beef. This layering of flavors is what gives the casserole its depth—I like to give this step a full minute to really develop the umami-rich base before adding the liquid.
Pour the beef broth into the pot and bring to a simmer, then add the elbow macaroni and stir to combine. Cover the pot and simmer for 5 minutes, stirring halfway through, then continue cooking covered for another 5 minutes. The pasta should be nearly tender but still have a slight bite to it—it will finish cooking when the cream is added, so don't overcook it here.
While the pasta cooks, shred the cheddar cheese (you should have about 4 cups total). In a small bowl, whisk together the sour cream and whole milk until smooth. Once the pasta is nearly tender, reduce the heat to medium-low and slowly pour in the sour cream and milk mixture, stirring constantly to prevent lumps from forming. Add 2½ cups of the shredded cheese in handfuls, stirring after each addition until fully melted and the sauce is smooth and creamy.
Sprinkle the remaining 1½ cups of shredded cheese over the top of the casserole in an even layer. Cover the pot and cook for 2-3 minutes on medium-low heat just until the cheese on top begins to melt slightly. Fresh sour cream in the sauce keeps everything wonderfully creamy, but I find that a light sprinkle of smoked paprika adds a subtle smoky note that takes this dish from good to memorable—feel free to add a pinch if you like. Remove from heat, garnish with fresh parsley, and serve immediately while hot and creamy.