Heat oven to 325°F with the racks in the upper middle and lower middle positions. Place paper liners into 2 (12-cup) muffin tins and set aside. If you prefer, set 12 oven-proof coffee mugs on a half sheet pan and set aside.
Whisk together the flour, baking powder and salt in a medium bowl. Set aside. Whisk together the hot water and the cocoa powder in a small bowl and set aside.
Combine the egg yolks and 2/3 cup plus 2 teaspoons (140 grams) of the sugar in the bowl of a stand mixer fitted with the whisk attachment. Beat on high until the mixture becomes pale yellow and forms ribbons when lifted, about 2 minutes. Add the cocoa mixture, vegetable oil, and vanilla and beat on medium speed to combine. Add the dry ingredients and beat on low speed just to combine. Transfer the mixture to a large bowl. Thoroughly clean the mixer bowl and attachment.
Place the egg whites and cream of tartar into the now-clean mixer bowl and beat on high using the whisk attachment until it becomes foamy. Decrease the speed to low and gradually add the remaining sugar. Once the sugar has all been added, increase the speed back to high and continue to beat until stiff peaks form, about 2 minutes.
Transfer one-third of the egg whites to the cake batter and whisk until well combined. Add the remaining egg whites and fold in gently.
Transfer the batter to the prepared muffin tins or coffee mugs, evenly dividing the batter between the cups. Place both muffin tins in 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 and 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.