Soak the breadcrumbs. In a mixing bowl, combine the breadcrumbs with the beaten egg and milk and let the mixture sit for 5-10 minutes, until the breadcrumbs are soft and have absorbed most of the liquid.
Mix the meatballs. Stir in the pesto, tomato paste, and garlic powder. Finally, use your hands to mix in the ground beef, salt, and pepper, until the mixture is just combined.
Scoop and broil the meatballs. Line a rimmed baking sheet with foil or parchment paper. Use a 2 Tbsp scoop to portion out the meatball mixture and roll them into balls. Place the meatballs on the prepared baking sheet. Move an oven rack to the top third of the oven and broil the meatballs on high for 6-8 minutes, until browned. Remove from the oven and let the meatballs cool slightly.
Make the soup. In a 4-5 qt dutch oven, heat the olive oil over medium heat. Once the oil is hot, add the diced onion, carrot, and celery and cook for 3-4 minutes, until the vegetables are soft and starting to brown. Add the garlic and cook a minute more. Stir in the tomato paste, dried oregano, red pepper flakes, and dried basil, and cook for 3-4 minutes until the tomato paste has darkened in color. Stir in the chicken stock, using a wooden or silicone spoon to scrape up any browned bits from the bottom of the pot.
Simmer the meatballs and pasta. Bring to a simmer and add the meatballs to the pot, leaving any fat on the baking sheet. Cover and simmer on low for 15 minutes. Remove the lid from the soup and stir in the pastina. Simmer for another 3-5 minutes, until the pasta is just barely tender. Stir in the fresh basil leaves and season to taste with salt and pepper.
Serve. Ladle the soup into bowls and top with a drizzle of olive oil, grated parm, and more fresh basil. Serve alongside crusty bread.