Crack the egg into a large mixing bowl and whisk lightly. Incorporate the ground beef, ground pork, bread crumbs, Parmesan, parsley, minced garlic, oregano, salt, and pepper. Combine the mixture thoroughly without overworking. Lightly coat hands with olive oil and shape the mixture into 1-inch meatballs using about 1 heaping teaspoon per meatball. Set aside on a plate or baking sheet; expect approximately 80 meatballs.

Warm the olive oil in a large Dutch oven or heavy-bottomed pot over medium heat. Working in two batches, sear the meatballs until browned on most sides, about 3 to 4 minutes per batch. Transfer to a paper towel-lined plate.

To the same pot, add the onion, diced carrots, and celery. Sauté the vegetables until they are beginning to soften but still retain some bite, roughly 10 minutes. Stir in the minced garlic, along with 1 teaspoon salt (use 2 teaspoons if the broth is low-sodium) and ½ teaspoon pepper. Cook for an additional minute until the garlic becomes aromatic.

Return the browned meatballs to the pot, pour in the chicken broth, and bring the soup to a simmer over medium-high heat. Stir in the pasta, reduce the heat, and let it simmer gently until the pasta is fully cooked, about 10 minutes.

Switch off the heat and mix in the spinach, stirring until the leaves have wilted. Taste and adjust seasoning as needed. Serve the soup hot, generously sprinkled with grated Parmesan. Note that the pasta will continue to absorb liquid over time; additional broth may be needed when reheating.