Craft the Meatballs: In a large bowl, combine all meatball ingredients. Mix gently by hand until just combined (do not overwork the meat). Roll into small, 1-tablespoon sized balls.
Brown the Meat: Option A (Oven): Roast at 350°F (180°C) for 20 minutes until golden.
Option B (Skillet): Pan-fry in a bit of oil over medium heat for 2-4 minutes per side until a crust forms. Set aside.
Sauté the Base: In a large Dutch oven or heavy pot, heat olive oil over medium-high heat. Add the onion, carrots, and celery. Cook for 5-10 minutes until the vegetables are tender and the onions are translucent.
Aromatics: Stir in the chopped garlic and red pepper flakes. Cook for just 1 minute until you can smell the fragrant garlic.
Build the Broth: Add the tomato paste and stir for a minute to "toast" it. Pour in the beef broth, diced tomatoes, and Italian seasoning. Bring the mixture to a rolling boil.
Simmer the Pasta & Meat: Add the broken spaghetti and the browned meatballs into the pot. Reduce heat to a simmer. Cook for about 10 minutes, or until the pasta is al dente.
The Finishing Touches: Taste and adjust salt and pepper. Stir in the 1/2 cup of Parmesan cheese and fresh parsley. For a final pop of flavor, stir in a tablespoon of balsamic vinegar right before serving.