For the mousse: Place a medium bowl in the freezer for 10 minutes. Meanwhile, melt the chocolate in a medium microwave-safe bowl on low power for 3 minutes. Let cool slightly. Pour the cream into the chilled bowl and whip until it holds stiff peaks. Fold one-third of the cream into the chocolate. Fold half of the remaining cream into the chocolate and then fold in the rest of the cream. Refrigerate until ready to use.
For the cones: Preheat a pizzelle iron.
Whisk together the flour, sugar, butter, milk, ginger, baking powder, cinnamon, cloves, salt, eggs and vanilla extract until smooth. Coat the pizzelle iron with the cooking spray, then close to continue heating.
When the iron is hot, spoon about 1 tablespoon of the batter onto each pizzelle well. Slowly close and let cook until golden, 50 seconds to 1 minute. Immediately roll one of the cookies around a wooden cone mold, slide it off, and transfer to a rack to cool completely. Leave the other cookie(s) on the iron while you work with the first one--they will firm up if you take them off the heat. Continue cooking and rolling in this way with the remaining batter.
Just before serving, fill a large resealable plastic bag with the mousse and snip off one corner. Dividing evenly, pipe the mousse into the cones. Serve immediately.