For the meatballs: Preheat the oven to 425 degrees F. Line a rimmed baking sheet with parchment and brush with oil.
Combine the parsley, garlic, carrot, celery and onions in a food processor and pulse to make an almost-smooth vegetable paste. Transfer to a large bowl. Add the eggs to the milk and whisk together, then add to the vegetables. Sprinkle with salt and pepper. Add the breadcrumbs, Parmesan, beef and pork. Mix well with your hands. Form into 6 large meatballs and place, without touching, on the prepared baking sheet. Bake until the meatballs are just cooked through, about 40 minutes.
For the marinara: Heat a large Dutch oven over medium heat, add the oil and onions and cook until softened, about 5 minutes. Add the garlic and red pepper flakes and cook until the garlic begins to sizzle but doesn't color, about 1 minute. Add the oregano, tomatoes, 1 teaspoon salt and 1 cup water and smash the tomatoes with the back of a wooden spoon. Lower the heat to a simmer and cook until slightly thickened and flavorful, about 20 minutes. Toss with the meatballs, then top with Parmesan and basil to serve.