Wash the leeks thoroughly between the layers, trim and cut into roughly 1 1/2-inch rounds or a height appropriate for your pan. Drain well and arrange upright in an 8-inch round oven-safe pan that fits your air fryer.
Melt the butter and anchovy paste in a saucepan. Add garlic and shallot and saute until softened.
Add wine and lemon juice and cook until reduced by half or more.
Add heavy cream and 1/4 cup Parmesan. Simmer over medium heat until slightly thickened, about 5 minutes. Season with salt and pepper to taste.
Pour the sauce over the leeks. Place the pan in the air fryer. In my Ninja Crispi 4-in-1, I remove the bottom tray and use AIR FRY, which has no selectable temperature setting. Follow your model instructions for pan placement.
Air fry for 30 minutes, until the leeks are soft and the sauce is bubbly. Check a larger round with a small knife; it should slide through easily. The tops will be very brown—those crispy, caramelized leek tops are exactly what we want!
Sprinkle with the remaining 1/4 cup Parmesan and air fry another 3–5 minutes to melt. Gently press any leeks that floated up back into the sauce.
Notes
Makes 6 side-dish servings. Prep takes about 5 minutes; the sauce takes about 10 minutes, followed by 33–35 minutes in the air fryer. Total time is about 48–50 minutes; the card displays the upper end of that range.
I have made this in both the Ninja Crispi 4-in-1 and Crispi Pro 6-in-1. The lake batch used AIR FRY on my 4-in-1, which has no selectable temperature. Cooking may vary with your model and the size of the leeks.
The very brown, crispy caramelized leek tops are intentional. Check that the centers are tender before adding the remaining Parmesan.