Prep the agnolotti. If using fresh or refrigerated agnolotti, keep them cold so they’re firm and easy to bread. Do not pre-boil.
Set up your breading station. Bowl 1: flour seasoned with 1/2 teaspoon salt and a few grinds of pepper. Bowl 2: beaten eggs.
Bowl 3: panko, Italian breadcrumbs, Parmesan, garlic powder, onion powder, smoked paprika, 1/2 teaspoon salt, and pepper.
Coat each piece. Dust agnolotti in flour, shake off excess, dip in egg, then press into the crumb mixture. Set on a tray. Repeat.
For extra crunch, press crumbs on firmly so they adhere.
Preheat the air fryer. 380°F (193°C) for 3–4 minutes. A warm basket helps crisping.
Load the basket. Lightly spray the basket and the crumbed agnolotti with oil. Arrange in a single layer with space between pieces.
Work in batches.
Air fry. Cook at 380°F for 6–8 minutes, flipping halfway and spraying again lightly. They’re done when golden brown and crisp. Thicker or larger agnolotti may need another minute.
Make the tomato-basil sauce. In a small saucepan or skillet, heat olive oil over medium-low.
Add garlic and cook 30 seconds. Stir in crushed tomatoes, basil, red pepper flakes, salt, and pepper. Simmer 5 minutes to meld.
Taste and adjust seasoning.
Make the lemon-parmesan aioli. In a bowl, mix mayo, garlic, lemon zest and juice, Parmesan, olive oil, salt, and pepper. Add a splash of water if you prefer it slightly thinner for dipping.
Serve. Pile the agnolotti on a platter. Sprinkle with extra Parmesan and a little chopped basil or parsley.
Serve with both sauces on the side for dipping.