In a medium saucepan combine the cream, 1/2 cup of the granulated sugar, vanilla extract and ginger. Bring to a boil, turn off the heat and let sit for 1 hour.
In a small bowl, combine the eggs and the remaining 1/2 cup sugar and beat to a homogeneous consistency.
Bring the cream-ginger mixture back to a boil and turn the heat off. Immediately strain and whisk a third of the cream mixture into the egg-sugar mixture and then immediately whisk the egg mixture back into the remaining cream mixture.
Chill the mixture over an ice water bath.
Churn the chilled mixture in an ice cream machine according to the manufacturer's directions.
Serve as is, or to make ice cream sandwiches, place 1 generous scoop of ice cream on the bottom of 1 Molasses Cookie and place another cookie on top. These can be done ahead and frozen. Let warm for 5 to10 minutes before serving.
Preheat the oven to 350 degrees F.
In medium bowl, combine the flour, baking soda, cinnamon, ginger, cloves and salt and set aside.
In the bowl of a standing mixer fitted with the paddle attachment, cream together the butter and brown sugar until light and fluffy. Beat in the egg and then the molasses. In thirds, gently mix in the flour mixture until just combined.
Using an ice cream scoop, scoop out the cookie dough into 1-inch balls onto a sheet tray covered with turbinado sugar. Gently toss the cookies in the sugar, covering them completely. Place the sugar-coated dough balls on another sheet tray and gently squish a little.
Bake for 9 to 10 minutes. Remove the cookies to a rack to cool.