Step 1: Preheat your oven to 350°F (175°C) and lightly grease a 2-quart baking dish.
Step 2: In a medium bowl, whisk together the flour, baking powder, baking soda, ground ginger, cinnamon, cloves, and salt for the apple cider and gingerbread pudding batter.
Step 3: In a large bowl, cream the 0.5 cup of softened butter and 0.5 cup of brown sugar until light and fluffy. Beat in the egg and molasses until well combined.
Step 4: Gradually add the dry ingredients to the butter mixture, alternating with the milk, and stir until just combined. Spread the batter evenly into the prepared baking dish.
Step 5: In a small saucepan, bring the apple cider, the remaining 0.5 cup of brown sugar, and 1 tablespoon of butter to a simmer, stirring until the sugar dissolves.
Step 6: Carefully pour the hot cider mixture over the back of a large spoon onto the batter in the dish. Do not stir.
Step 7: Bake for 40-45 minutes, or until the center of the apple cider and gingerbread pudding cake is set and the sauce is bubbling around the edges.
Step 8: Let the apple cider and gingerbread pudding stand for 10 minutes before serving warm with ice cream or whipped cream.