Mix pork, beef, egg white, bread crumbs, and Italian seasoning together in a bowl. Form very small, pea-sized meatballs.
Heat oil in a soup pot or Dutch oven over medium heat. Add carrots, celery, parsnip, onion, herbes de Provence, red pepper flakes, salt, and pepper. Cook and stir until vegetables are soft, 7 to 10 minutes.
Pour chicken broth into the pot; bring to a boil. Add the mini meatballs and orzo pasta. Reduce heat to low; let simmer until flavors combine, 15 to 20 minutes. Add spinach; cook until wilted, 2 to 3 minutes. Garnish with Parmesan cheese.