Pat the chicken dry — really dry. This is the single most important step for getting a crust in the air fryer, and most recipes skim past it. Wet chicken steams. Dry chicken sears.
Drizzle the oil over both sides, then sprinkle on all the spices. Use your hands. Get under the breasts, on the sides, everywhere.
Preheat to 380°F. While it heats, you've got two minutes to start the sauce.
Put the chicken in the basket in a single layer. Do not stack. If you have to cook in batches, cook in batches — the foil-tent will keep batch one warm.
12 minutes total, flip at 6. Pull when an instant-read thermometer hits 165°F at the thickest point. Let it rest 5 minutes before slicing. Resting matters; cutting too early dumps all the juice onto your cutting board.
Medium heat, large skillet. Melt the butter. Once it's foaming, add the garlic and chopped sun-dried tomatoes. Ninety seconds — you're after fragrant, not browned. Browned garlic is bitter garlic.
Pour in the chicken broth. It'll bubble hard for a second. Scrape the bottom of the pan with a wooden spoon to lift any fond — that's flavor.
Add the cream, Parmesan, Italian seasoning, and red pepper flakes. Reduce to medium-low. Stir often for 4–5 minutes. The sauce is done when you can drag a spoon through it and the line holds for a second before closing.
Slice the rested chicken on a slight bias. Lay the slices in the sauce so the bottom edge soaks up some sauce, then spoon more over the top. Tear basil over everything. Eat immediately.