In a large pot or Dutch oven, brown the ground beef over medium heat until fully cooked, about 5-7 minutes. Drain any excess fat.
Add the diced onion, minced garlic, carrots, and celery to the pot. Sauté for about 5 minutes until the vegetables start to soften.
Pour in the chicken broth and bring the mixture to a boil.
Stir in the elbow macaroni and reduce heat to a simmer. Cook for about 8-10 minutes, or until the macaroni is al dente, stirring occasionally.
Once the pasta is cooked, reduce the heat to low, and stir in the shredded cheddar cheese and milk. Mix until the cheese is melted and the soup is creamy.
Add Worcestershire sauce, paprika, salt, and pepper to taste. Stir well to combine.
Ladle the soup into bowls and garnish with fresh parsley if desired. Serve hot.
For variations, feel free to customize the vegetables according to your preference, or add a pinch of cayenne pepper or some diced jalapeños for spice.
Store leftover soup in the refrigerator for up to 3 days. Reheat on the stove over medium-low heat before serving.