Heat oven to 325°F. Place paper liners into 2 (12-cup) muffin tins and set aside. If you prefer, set 12 ovenproof coffee mugs on a half sheet pan and set aside.
Whisk together the flour, baking powder and salt in a medium mixing bowl. Set aside.
Place the egg yolks and 5 ounces (142 grams) of the sugar into the bowl of a stand mixer and whisk on high until the mixture becomes pale yellow and 'ribbons' when lifted, about 2 minutes. Add the water, vegetable oil, and vanilla and whisk to combine. Add the dry ingredients and whisk just to combine. Transfer the batter to a mixing bowl while you whisk the egg whites.
Place the egg whites and cream of tartar into a clean bowl and whisk on high using the whisk attachment, until it becomes foamy. Decrease the speed to low, and gradually add the remaining ounce (28 grams) of sugar. Increase speed to high and continue whisking until stiff peaks form, about 2 minutes.
Transfer one third of the egg whites to the batter and whisk until well combined. Add the remaining egg whites and fold in gently. Transfer batter into prepared muffin tins or coffee mugs, evenly dividing the batter between the cups. Place both muffin tins on the middle rack of the oven or, if using mugs, place all of them on a half sheet pan and set on the bottom rack of the oven. Bake until a toothpick comes out clean or the cupcakes reach an internal temperature of 205 to 210°F, about 30 minutes. Remove from the oven to a cooling rack and allow to cool completely before frosting.