Preheat oven to 350 degrees Fahrenheit. Line a muffin tin with cupcake liners and set aside. Sift the flour, cocoa powder, baking soda, and salt in a medium-sized mixing bowl and set aside as you prepare the wet ingredients.
In a large mixing bowl, whisk together the melted butter and granulated sugar until creamed. Whisk in the Greek yogurt. Then mix in the eggs one at a time. Add the sourdough discard, warm water, and vanilla extract.
Add half the dry ingredients to the bowl of wet ingredients, mixing until just combined. Add the second half and mix again until it is just combined.
Scoop batter into each muffin tin, filling each 3/4 full with batter.
Bake for about 18 minutes. This recipe makes 18 cupcakes. The cupcakes are ready when you stick a toothpick in the center of them and no wet batter sticks to the toothpick. Let the cupcakes cool completely before frosting them.