Preheat oven to 350ºF. Line a 9"x9" baking pan with foil.
Melt 2 tablespoons of butter in a small saucepan. Add the apples and cook until softened, about 5 minutes.
In a large mixing bowl, beat together the butter and sugar until light and fluffy. Mix in the egg, then add the molasses.
In a second bowl, mix together the flour, baking soda, and spices. Stir half of the dry ingredients into the butter and sugar mixture; mix until combined. Stir in the hot water. Add the remaining dry ingredients and mix until combined (the batter will be smooth and light brown, similar to milk chocolate frosting). Stir in the apples and crystallized ginger.
Pour into the prepared baking pan and bake for about 1 hour 15 minutes, or until a toothpick inserted into the center of the cake comes out clean.