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Step 1
Put the cream, thyme, cayenne, garlic, 1/2 teaspoon salt and several grinds of black pepper in a small saucepan over medium heat. Bring to a gentle simmer, stirring often, and cook for 1 minute; turn off the heat.
Step 2
Thinly slice the sweet potatoes on a mandoline or vegetable slicer into about 1/8-inch-thick rounds. Arrange a third of the potato slices in a single, overlapping layer in a 7-inch nonstick cake pan (see Cook's Note). Spoon over a third of the cream mixture, then sprinkle with a pinch of salt and 1 tablespoon of the Parmesan. Repeat with another third of the slices, third of the cream mixture, a pinch of salt and 1 tablespoon Parmesan. Finish with the remaining slices and cream, another pinch of salt and the remaining 1 tablespoon Parmesan.
Step 3
Cover the cake pan tightly with foil and place in the basket of a 6-quart air fryer. Air fry at 400 degrees F until the potatoes are tender and easily pierced with a knife and the cream mixture is bubbling along the sides, about 45 minutes.
Step 4
Meanwhile, mix the panko, pecans and olive oil in a small bowl. Remove the foil from the cake pan and sprinkle over the panko mixture. Return to the air fryer basket and air fry at 400 degrees F until golden brown, 3 to 4 minutes. Let rest for 5 minutes, then top with the chopped chives.