In the bowl of a stand mixer, combine sugar and butter and beat until combined. Beat in egg and molasses.
Add flour, ginger, baking soda, cinnamon and beat until completely combined (mixture will be stiff). Cover and refrigerate at least 3 hours.
Make the truffles. Combine chocolate and cream in a microwave-safe container and microwave on low heat for 30-45 seconds. Remove from the microwave and stir until melted, putting back in the microwave for another 10-15 seconds if necessary, repeat until smooth.
Refrigerate until completely chilled (3-4 hours).
Add 1-2 tbsp icing sugar as necessary until the truffles are able to be rolled into balls. You don't want them too thick or thin -- you want them to still be soft when cookies are room temperature but not so soft that they will leak out.
Roll chocolate into ½" truffles and cover in icing sugar. Freeze 1 hour or until firm.
Make your cookies: Shape dough into roughly 1" balls and flatten the middle with your thumb. Place a frozen truffle in the middle and roll the dough around it, being careful not to leave any holes or gaps for it to leak. Roll cookie in granulated sugar and place on a cookie sheet at least 2" apart.
Bake at 350 degrees F for 8-10 minutes, until set. Cool slightly, then do yourself a favour and eat one fresh out of the oven.