Preheat oven to 375 degrees F (190 degrees C). Line 36 muffin cups with paper liners.
In a large bowl, mix together the flour, sugar, cocoa, baking soda and 1 teaspoon salt. Make a well in the center and pour in the eggs, 1 cup milk, water, oil and 1 teaspoon vanilla. Mix well. Fill each muffin cup half-full of batter.
Bake in the preheated oven for 15 to 20 minutes, or until a toothpick inserted into the center of the cake comes out clean. Allow to cool.
Make filling: In a large bowl, beat butter and shortening together until smooth. Blend in confectioners' sugar and pinch of salt. Gradually beat in 3 tablespoons milk and 1 teaspoon vanilla. beat until light and fluffy. Fill a pastry bag with a small tip. Push tip through bottom of paper liner to fill each cupcake.