Preheat your oven to 300°F. Line two baking sheets with parchment paper and lightly spray them with nonstick spray.
Separate the eggs into two bowls: whites in a medium bowl and yolks in a large bowl.
Using an electric whisk, whip the egg whites and cream of tartar until stiff.
Whisk the egg yolks, Greek yogurt, and salt until smooth.
Using a spatula, carefully fold the egg whites into the yolk mixture, working in batches. Work by placing a mound of egg whites on top of the yolk mixture, then gently fold the yolk mixture from under and over the egg whites. Fold again and again until incorporated.
Repeat with more egg white mounds until the entire mixture is fully incorporated.
Using a ¼ cup ice cream scoop or measuring cup, spoon 5-6 large mounds of the mixture onto each of the prepared baking sheets.
Gently press each mound with a spatula to flatten it slightly.
Bake until golden brown and set, about 30 minutes. Cool the bread pieces on the cookie sheet for a few minutes, then gently transfer them to a wire rack to cool completely. Alternatively, you can use them while still warm.
Video
Notes
You can replace the Greek yogurt with softened cream cheese, sour cream, or mayonnaise.
Fat interferes with whipping egg whites. Please ensure there's no yolk mixed into the egg whites, and use a thoroughly clean and dry bowl and whisks to whip them.
The cream of tartar helps stabilize the whipped egg whites, so I highly recommend using it. You can usually find it in the spice aisle in any supermarket.
Folding egg whites is a technique that incorporates whipped egg whites into a thicker mixture (such as a cake batter or, in our case, a yolk/yogurt mixture) without breaking the tiny air bubbles that make them fluffy and airy. The technique involves placing a mound of whipped egg whites on the thicker mixture and using a spatula to repeatedly scoop the thicker mixture and fold it over the whipped egg whites. When this mound has been incorporated into the batter, add another mound of egg whites. Unlike stirring, this technique ensures that the batter remains airy and fluffy.
Leftovers: Cloud bread is best made right before you plan to eat it. It gets soggy when stored in the fridge. However, you can freeze it, its layers separated with wax paper squares, and gently defrost it in the microwave.