Preheat your oven to 300°F and line a large baking sheet with parchment paper.
In a large clean bowl, beat the egg whites and cream of tartar with an electric mixer on high speed until stiff, glossy peaks form. This usually takes about 3 to 4 minutes. The peaks should stand straight up when you lift the beaters.
In a separate bowl, whisk together the egg yolks, softened cream cheese, and salt until completely smooth and creamy. Make sure there are no lumps of cream cheese remaining.
Gently fold the egg yolk mixture into the whipped egg whites using a rubber spatula. Use slow, sweeping motions from the bottom to the top of the bowl, rotating the bowl as you go. Be very careful not to deflate the whites.
Spoon the mixture into 6 even mounds on the prepared baking sheet, spacing them about 2 inches apart. Each round should be roughly 4 inches wide and about 3/4 inch thick. Smooth the tops gently with the back of the spoon.
Bake for 25 to 28 minutes until the tops are golden and the rounds feel set when lightly tapped. Let them cool completely on the baking sheet before lifting them off the parchment. Cloud bread firms up significantly as it cools.
