In a small saucepan, heat oil over medium-high heat. Add onion and garlic; cook and stir until tender, 3-4 minutes. Stir in tomato puree, basil, salt and pepper. Bring to a boil; reduce heat. Simmer, uncovered, 10 minutes. Keep warm.
Meanwhile, preheat air fryer to 350°. In a small bowl, whisk eggs and milk. In another bowl, combine bread crumbs, garlic powder, cheese, parsley and salt.
Dip tortellini in egg mixture, then in bread crumb mixture to coat. In batches, arrange tortellini in a single layer in greased air-fryer basket; spritz with cooking spray. Cook until golden brown, 4-5 minutes. Turn; spritz with cooking spray. Cook until golden brown, 4-5 minutes longer. Serve with sauce; sprinkle with additional minced fresh basil.