For the eggplant
Preheat the air fryer to 320°F for 5 minutes.
Place the eggplant in a large bowl, drizzle with olive oil, and add a healthy pinch of salt and pepper. Stir to coat.
Transfer the eggplant to the cake barrel and set it in the fry basket. Cook for 10 minutes.
Add the tomatoes, onion, garlic, and ½ cup water. Cook for another 10 minutes.
Stir, adding another ½ cup water, and cook for 5 minutes. Reduce the temperature to 260°F and cook until the eggplant is tender, 5–6 minutes more. If it looks too dry, add a little more water or tomatoes. Cooking times will vary depending on machine, but overall, this recipe should take about 30 minutes to cook. Transfer to a bowl and cover to keep warm while you prepare the polenta.
Stir in the fresh basil before serving on top of sliced polenta. Sprinkle with more fresh basil for garnish.
For the polenta
Preheat the air fryer to 400°F.
Slice the polenta into ½-inch-thick discs. Spray with a little cooking spray and place them in the fry basket. Cook for 20 minutes and flip them over. Sprinkle with the cheese and spray with a little cooking spray (not too close or the cheese will fly around). Cook until the edges become crispy, 10 minutes more.