Beat the shortening and sugar in the bowl of an electric mixer on medium speed for about 2 minutes, until creamy. Add the egg and molasses and mix well to combine.
Whisk together the flour, ginger, cinnamon, nutmeg, cloves, and salt in a medium bowl. Stir together the boiling water and baking soda in another bowl. Add the flour and water mixtures alternately to the batter, beginning and ending with the flour mixture, and mix until just combined. Cover the dough with plastic wrap and chill in the refrigerator overnight.
Preheat the oven to 400°F and line a few baking sheets with parchment paper. Using a small ice cream scoop, drop the dough onto the baking sheets, spacing the cookies 1-inch apart. Bake for 8 to 10 minutes, until the cookies spring back when pressed gently with your finger. Remove from the oven and let cool for 5 minutes. Transfer the cookies to wire racks and let cool completely.
Beat the butter and powdered sugar in the bowl of an electric mixer on medium speed for about 2 minutes, until creamy. Add the milk and vanilla extract and beat until smooth.
Spread the filling on the flat side of half of the cookies. Place another cookie, flat side down, on top of the filling and press down gently.