To make the molasses mixture: In a tall 6-quart pan, bring the water and molasses to a boil. Remove from heat and stir in the baking soda. The mixture will foam up. Set aside to cool.
In a small saucepan, bring the apricots and 1 cup of the apple cider to a boil. Remove from heat and let the apricots plump for about 20 minutes.
Preheat the oven to 350 degrees F. Spray a 9 by 13-inch baking dish with vegetable oil cooking spray.
In a medium saucepan, blend the brown sugar and cornstarch. Stir in the remaining 1/2 cup apple cider, the butter, cinnamon, salt, and cloves. Cook over medium heat until clear and thickened. Stir in all but 1/4 cup of the plumped apricots. Stir in all but 3/4 cup of the apples. Pour the mixture into the prepared dish; set aside.
To make the cake layer: Sift the flour, ginger, baking powder, cinnamon, cloves, allspice, pepper, and salt together into a medium bowl; set aside.
In a mixer bowl, using the mixer on high speed, cream the brown sugar and butter until light and fluffy. Add the egg, beating until creamy. On low speed, alternately blend in the dry ingredients and the molasses mixture. The batter will be thin. Stir in the reserved apricots and apples. Pour the cake batter over the fruit layer in the baking dish. Bake for 40 to 45 minutes, or until a toothpick inserted just into the cake layer comes out clean. Let cool slightly and serve with whipped cream.
Recipe courtesy of Cory Schreiber, Wildwood, Ten Speed Press, 2000