Preheat the oven to 350 F. Line a cupcake pan with liners.
Add dry ingredients into a large mixing bowl, or the bowl of a stand mixer. Cream the butter (1/2 cup butter) into the dry ingredients. (1 1/4 cup cake flour, 1/2 cup cocoa powder, 1/4 teaspoon baking soda, 3/4 teaspoon baking powder, 3/4 cup sugar, 1/4 teaspoon salt)
Mix in the 1/2 cup of oil. Mix in the eggs (2), one at a time. Add the 1/2 cup of hot water and mix in. Pour the batter into the cupcake pan, filling each well about 2/3 of the way full. If you want, you can first pour the batter into a large glass measuring cup, making it easier to fill the wells.
Bake cupcakes for 18-22 minutes, or until a toothpick inserted in the middle comes out mostly clean. Let them sit for 10 minutes, then turn them out onto a cooling rack to cool completely. You want to be sure the cupcakes are fully cooled off before frosting. I like to put mine in the fridge once they have cooled down from the oven.