In a large bowl, cream the butter and sugar until light in fluffy. Beat in egg, molasses, lemon juice, lemon zest, and vanilla.
In a medium bowl, combine flour, ginger, baking soda, cinnamon, cloves, cardamom, and salt. Gradually add the flour mixture into the butter mixture and mix well.
Remove dough from bowl and wrap in plastic wrap and refrigerate overnight.
When you're ready to make the cookies, working quickly on a floured marble pastry board, remove dough from fridge and section half off to roll out with a Rolling Pin. Roll to 1/4 inch thickness and then using desired shapes, cut out your shapes and place on a Silpat Cookie Sheet.
Repeat process until dough is used up.
Bake in the oven for 8-9 minutes on the top rack, removing promptly and setting the cookies while on their silpat on a Cooling Rack .
When completely cooled (about 30 minutes-1 hour) you can begin frosting.
For the frosting
In a metal bowl, combine all ingredients and stir together until your frosting has a runny consistency.
Place in a Piping Bag and pipe desired designs onto your cookies.