Meanwhile, make the orzo. Heat the olive oil in a large high-rimmed sauté pan. Add the diced onions, carrots, and celery. Cook for about 5 minutes, stirring occasionally until the vegetables have softened.
Add the garlic, stir, and cook for another minute. Add the uncooked orzo, stir, and toast for another minute. Pour in the white wine to deglaze the pan. Scrape any stuck bits from the bottom of the pan with a wooden spoon. Simmer for a minute until most of the wine is absorbed.
Pour in the beef bone broth, chicken broth/water, black pepper, and dry mustard. Bring to a boil. Lower to a simmer and cook until the orzo is cooked through and most of the liquid is absorbed. Stir often so the orzo doesn't stick to the bottom of the pan. Add additional broth/water as needed if it absorbs before the orzo is cooked. This will take about 15 minutes.
Once the orzo is cooked, turn the heat to low. Add the freshly grated parmesan cheese and stir until combined and melted. Stir in the spinach/arugula and stir until wilted. Finally, mix in the baked meatballs.
Divide among bowls to serve. Top with freshly grated parmesan cheese and cracked black pepper as desired.