Start by gathering all the ingredients. Preheat your oven to 350°F and position the rack in the middle. Line a standard 12-cup muffin tin with cupcake liners, then lightly coat them with cooking spray to prevent sticking.
In a large bowl, combine the flour, cocoa powder, baking soda, baking powder, and salt. Whisk them together thoroughly, ensuring there are no clumps. Set this dry mixture aside for later.
In a separate medium-sized bowl, whisk the eggs and sugar until they become pale and slightly frothy. Stir in the Greek yogurt, vegetable oil, and vanilla extract, mixing until smooth and well-incorporated.
As you whisk, slowly drizzle the boiling water into the wet mixture, blending until the mixture is smooth and the water is fully incorporated. Be sure to pour the water gradually to avoid splashing.
Carefully fold the wet mixture into the dry ingredients using a rubber spatula. Stir gently until the batter is smooth, making sure no pockets of dry flour remain.
Using a 1/2-cup measuring cup, evenly distribute the batter into the prepared cupcake liners. Fill each about two-thirds full.
Bake for 20 to 25 minutes, or until a toothpick inserted into the center of a cupcake comes out with just a few moist crumbs attached. Allow the cupcakes to cool in the pan for about 5 minutes before transferring them to a wire rack to cool completely.
Once cooled, feel free to frost, glaze, or top the cupcakes with your preferred decorations. Enjoy!