In your mixer, combine butter, shortening and sugar until light and fluffy, about 3 minutes. Add in egg, molasses and orange peel. Beat until blended.
Stir flour, baking soda, ground ginger, cinnamon, cloves and salt together in a medium bowl.
Add dry ingredients to wet ingredients and mix until just incorporated. Cover and chill for 1 hour.
Preheat oven to 350° and grease 2 baking sheets (or line with silicone baking sheet). Place sugar in small bowl. Form cookie dough into 24 equal balls (about ***). Roll each ball in sugar and transfer to prepared baking sheet. Bake for 12-15 minutes. Cookies should be cracked on top, but still soft.
In a large bowl, combine all ingredients. Stir until sugar has dissolved. Pour into an Ice Cream Maker and freeze according to the maker's instructions.
Ice Cream Sandwiches
Place 12 cookies onto your work surface. Make sure the flat side is facing up. Top each cookie with about ⅓ cup of ice cream. Spread the ice cream out evenly, but not to the very edge, leave about ¼ inch. Top the ice cream with a second cookie.
Place cookie sandwiches in the freezer for about 2 hours. Keep frozen until serving*.
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*If you are planning on storing these in your freezer for more than a day sandwiches will need to be wrapped in order to preserve. Allow them to freeze for 2 hours, then remove from freezer and wrap individually in plastic wrap. Return to the freezer until ready to eat.