Step 1

Preheat the air fryer to 375 degrees. Crumple a 16x12-inch piece of parchment paper, smooth it out and use it to line a 6x3-inch springform pan or one with a removable bottom. Crease the paper at the edges, pinching it, so it folds over, and use your fingers to press the paper down as best you can so it snugly hugs the bottom and sides of the pan.

Step 2

In a food processor, process the eggs and sugar until smooth, about 30 seconds. Scatter the cream cheese pieces evenly over the sugar and egg mixture in the bowl. Pour in the cream and vanilla, and sprinkle in the flour and salt. Process until smooth and combined, another 30 to 45 seconds.

Step 3

Pour the batter into the prepared pan and carefully transfer the hot air fryer basket. (You may need to make a sling out of foil to lower and lift the baking pan, as it may be snug.) Bake for about 25 minutes. At the 15-minute mark, check on the cake and, if it is already quite dark, cover the top with a larger cake pan that fits over it or a piece of foil. The cake is ready when a thermometer inserted into the center of the cake reads about 155 degrees, and the edges are set but the middle still slightly jiggles. Carefully transfer the pan to a wire rack and let cool until slightly warm or completely, about 1 hour.

Step 4

Remove the sides of the pan and slide the cake, plus the papered bottom of the pan, onto a serving plate. Slice into 8 pieces, dipping the knife into hot water and drying it in between slices, and serve. The cake can be tightly wrapped and refrigerated once it has cooled completely, but should be brought to room temperature again before serving.