For the ginger cookie crust: Preheat the oven to 350 degrees F. Lightly grease a 9-by-2-inch cake pan (you can use a springform pan, but you will need to wrap the bottom in foil to bake it in the water bath) or a 9-inch heart-shaped pan.
In a food processor, chop up the cookies until they are powdery. Mix in the butter, brown sugar and salt. Pour the cookie crumbs into the prepared pan and press them tightly into the bottom of the pan. Bake just until it sets and smells toasty, about 10 minutes. Allow to cool while you make the batter.
For the cheesecake: In a stand mixer, beat the honey, cornstarch, flour and egg yolks until lightened, about 1 minute. Add the cream cheese, ricotta, ginger extract if using, vanilla extract and lemon zest to the egg mixture and beat on medium speed until it is smooth and creamy, about 2 minutes.
In a separate bowl, beat the egg whites and sugar to glossy, stiff peaks. Stir one-third of the whites into the cheesecake batter. Fold another third of the whites into the batter. Gently fold the remaining whites into the batter.
Spread the cheesecake batter over the crust and smooth the top. Place the cake pan in a large baking dish. Pour hot water into the baking dish so that it goes halfway up the side of the cheesecake pan. Carefully place it in the oven and bake for about an hour. If the cake is not done at the end of the hour (you will know by carefully touching the top to see if it feels set up), reduce the heat to 300 degrees F and bake for another 15 minutes, then check to see if it is done. The speed of the baking will depend on the type of pan you use and how hot the water is when you pour it into the pan. It can take up to 1 1/2 hours. This style cheesecake will crack a bit.
Remove the cake from the oven when it is set, but leave it in the water bath until it has cooled to nearly room temperature. To prevent large cracks in the middle of the cake, run a sharp paring knife around the edge of the cake to separate it from the pan. Once the cake is cooled, refrigerate it for at least 5 hours.
For the cherry topping: In a saucepan, cook together the cherries, sugar, cornstarch, water (or wine), lemon juice, vanilla extract and cardamom extract. Cook over low heat until it comes to a boil and the cornstarch turns translucent. Transfer to a bowl and place in the refrigerator to cool and thicken.
Remove the cheesecake from the pan by putting the pan over low heat on the stove for several seconds, then running the paring knife around the edge, covering the pan with plastic wrap and inverting the pan onto a flat plate. If the cake won't come out easily, quickly remove the plastic and place it over the heat again. It should slip right out. Once it is out, invert the cake onto the serving platter.
Spoon the cooled cherry topping over the cheesecake and serve, or keep in the refrigerator until ready to cut.