Preheat the oven to 350 °F and line a cupcake pan with liners.
In a large mixing bowl, combine flour, sugar, cocoa powder, baking soda, and salt.
Beat the egg.
In a separate bowl, whisk together the yogurt, oil, vanilla, and beaten egg. It's okay if there is some separation between the yogurt and oil.
Make a well in the dry ingredients and add the wet ingredients. Mix together until just combined.
Add the boiling water last. Mix until smooth.
Bake for 18 minutes or until a toothpick comes out clean.
Let cool completely before filling.