Preheat oven to 350°F. Grease a 9-inch square pan with butter and set aside.
For the cake, in a medium bowl, whisk together the flour, baking soda, ginger, cinnamon, cloves, salt, and candied ginger until blended, then set aside. In a separate bowl, mix the molasses and hot water.
In a large bowl, using a hand or stand mixer fitted with the paddle attachment, beat the butter on high speed until smooth and creamy, 1 minute. Add the brown sugar and beat on high speed for 1 minute until creamy. Scrape down the sides and bottom of the bowl with a rubber spatula. On medium-high speed, add the egg and vanilla until blended. Scrape down the sides and bottom of the bowl with a rubber spatula. With mixer on low speed, add dry ingredients in three additions, alternating with hot water/molasses, beginning and ending with dry ingredients, mixing each addition until incorporated. Do not over mix. The dough will be thin. Beat any large lumps.
Pour the dough into the buttered mold. Bake for approximately 35 minutes or until the cake is fully baked. To test if it’s done, insert a toothpick into the center of the cake. If it comes out clean, it’s done. Let the cake cool completely in the pan on a wire rack. The cake must be completely cool before frosting.
For the frosting, in a large bowl, using a hand mixer or stand mixer fitted with a paddle attachment, beat together the cream cheese and butter on medium-high speed until creamy and smooth, 2 minutes. Add icing sugar, lemon juice and lemon zest. Beat on low speed for 20 seconds, then increase to high speed until everything is completely combined and the frosting is creamy. Spread over the cake. Spread around the sides if you have extra frosting.
For the crust, bring a medium pot of water to a boil. Once the water boils, reduce the heat to medium-low.
Meanwhile, line a baking sheet with parchment paper. Combine the blueberries, ginger, and hazelnuts in a bowl.
Chop white chocolate into equal size pieces and place in a medium stainless steel bowl. Place it over the pot of boiling water, making sure it doesn’t touch the water. Using a rubber spatula, stir occasionally until more than half of the chocolate has melted. Remove container from heat; the remaining heat will melt the rest of the chocolate. Add the salt and stir to evenly incorporate and finish melting the chocolate.
Pour the melted chocolate onto the prepared baking sheet and spread it into a ½-inch-thick layer. Sprinkle over the blueberry-ginger-hazelnut mixture. Gently press into the chocolate. Place the baking sheet in the refrigerator for 20 to 30 minutes until the chocolate sets. Break into pieces and decorate the cake.