Spray a 9-inch spring form pan with nonstick cooking spray. Line the bottom and sides of the pan with parchment paper, and lightly spray the paper. Preheat oven to 350 degrees F.
Beat the egg whites on high speed with the salt and cream of tartar until foamy. With the mixer running, gradually add ½ cup of sugar and beat until stiff peaks form.
In a separate mixing bowl, beat the egg yolks and 1 cup sugar on high speed until very fluffy and light in color. Add almond flour and orange zest and beat until fully incorporated.
Stir ⅓ of the egg whites into the yolk mixture. Fold in the remaining egg whites, half at a time, until the mixture is no longer streaky.
Pour into the prepared pan and bake for 20 minutes. Then, gently lay a piece of foil over the top of the cake, and bake for another 10 to 15 minutes. The cake should be golden brown and puffed. (As the cake cools, the center will sink in.)