Combine the brown sugar, shortening and molasses in a large bowl and mix until smooth. Add in the egg and beat until combined.
Add in the baking soda, ginger, cinnamon, cloves and nutmeg. Mix to combine. Add in the flour and beat together. The dough will start to come together but will look crumbly. Beat until it sticks together when you squeeze it together with your fingers.
Place the sugar in a small bowl. Make 1-inch balls from the dough, then roll in the sugar. Place at least 2 inches apart on baking sheets. Bake 9-11 minutes, until the cookies are just set and starting to crack on the edges.
Remove from the oven and immediately press the centers down with the handle of a wooden spoon, creating an indentation. Cool for a minute or two on the cookie sheets, then remove to a wire rack to cool completely.
In a bowl, whisk together the cocoa powder, powdered sugar, hot water and vanilla. Fill each cookie with the chocolate mixture, then sprinkle with turbinado sugar. Let the chocolate set up before storing in an airtight container.