Preheat the oven to 375 degrees F (190 degrees C). Line 36 muffin cups with paper liners.

Prepare the cupcakes: Mix together flour, sugar, cocoa, baking soda, and salt in a large bowl. Make a well in the center and pour in eggs, milk, water, oil, and vanilla. Mix well.

Fill each muffin cup halfway with batter.

Bake in the preheated oven until a toothpick inserted into the center of the cake comes out clean, 15 to 20 minutes. Allow to cool.

Make filling: Beat butter and shortening together in a large bowl until smooth. Blend in confectioners' sugar and salt. Gradually beat in milk and vanilla. Beat until light and fluffy. Place filling into a pastry bag with a small tip.

Once cupcakes have cooled, push tip through bottom of paper liner to fill each cupcake.