Add all of the meatball ingredients to a large bowl and mix just until combined. Form the mixture into about 25 mini meatballs.
Heat 2 tbsp avocado oil in a large pot over medium-high heat. Add the meatballs and cook, turning occasionally, until lightly browned on all sides. They do not need to be fully cooked through at this point. Remove from the pot and set aside.
Add the onion, carrot, and red bell pepper to the same pot. Cook for about 4–5 minutes, then add the garlic and continue cooking until the vegetables are softened and lightly caramelized, about 1–2 more minutes.
Add the salt, black pepper, Italian seasoning, paprika, and cayenne, if using. Stir and cook for about 30 seconds, until the vegetables are evenly coated and the seasonings are fragrant.
Add the tomatoes and use a wooden spoon to break them into smaller pieces. Stir in the tomato paste, balsamic vinegar, and sugar.
Bring the tomato mixture to a simmer and cook uncovered for 15–30 minutes, stirring occasionally, until the tomatoes have broken down, the juices have reduced, and the flavors are concentrated.
Pour in the chicken stock and stir to combine. Bring to a boil, then cover, reduce the heat, and simmer for 10 minutes.
Remove the lid and use an immersion blender to blend the soup until smooth.
Add the browned meatballs back to the pot along with the uncooked orzo. Continue to simmer uncovered for 12–15 minutes, stirring occasionally, until the meatballs are cooked through, the orzo is tender, and the soup has thickened.
Ladle into bowls and serve warm. Enjoy as is or top with freshly grated Parmesan cheese, if desired.