Preheat the oven to 400 degrees F. Line a baking sheet with aluminum foil.
For the meatballs and pasta: Heat the oil in a large skillet over medium-high heat. Add the spinach and cook, stirring, until wilted and tender, 3 to 4 minutes. Transfer to a cutting board to cool slightly, then chop the spinach finely.
Meanwhile, combine the chicken, veal, breadcrumbs, milk, Parmigiano-Reggiano, garlic powder, onion powder, ketchup, brown sugar, egg, salt and pepper and spinach in a large mixing bowl. Use your hands to gently mix the ingredients until just combined. Gently roll the mixture into balls about 1 1/2 inches in diameter and place them on the prepared baking sheet; if the mixture is too loose, mix in a little more breadcrumbs.
Bake the meatballs until cooked through, about 22 to 24 minutes. Switch the oven to broil; broil the meatballs on high until browned, 4 to 5 minutes.
Meanwhile, bring a large pot of salted water to a boil and cook the pasta according to package instructions for al dente. Drain, reserving some of the pasta cooking water. Put the pasta back in the pot.
For the cashew pesto: Combine the basil, garlic, cashews, Parmigiano-Reggiano, oil, 1/4 cup water and salt and pepper in a blender and blend until smooth.
Gently toss the hot pasta with the pesto in the pot, adding some pasta cooking water if necessary for a creamy sauce. Top with the meatballs. Drizzle with olive oil and enjoy!