Preheat the oven to 325 degrees F (165 degrees C). Grease 16 muffin cups.

Stir flour, 1 cup sugar, baking powder, and salt together in a large bowl until well combined. Make a well in the center and add oil, egg yolks, orange peel, vanilla, orange juice, and water. Mix well by hand until smooth with no lumps. Set aside.

Beat egg whites and cream of tartar in a large glass or metal mixing bowl until foamy. Gradually add 1/2 cup sugar, continuing to beat until soft peaks form. Lift your beater or whisk straight up: egg whites should form soft mounds rather than a sharp peak.

Fold flour mixture into egg whites until incorporated. Pour batter into the prepared muffin cups to about 2/3 full.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 40 minutes. Cool in the pans for 10 minutes before removing to cool completely on a wire rack.