Make the topping: Boil Lemon, sugar, and water. Reduce by half, stirring occasionally. Add in the blueberries and cook until well coated and the syrup becomes blue. It should not be runny. Remove from heat and refrigerate.
Preheat oven to 325.
make the crust: Pulse the graham crackers in a food processor until smooth. Add in all dry ingredients. Then drizzle in butter while the machine is on. The crumbs should hold their shape, and not crumble much.
Assemble and spray a spring form pan. Place it on a sheet pan in case anything leaks out.
Press the crumb crust into the bottom of the pan in a flat even surface. Bake at 325 for 10 minutes while you are making the filling, so that it crisps the crust a bit.
make the filling: Pulse the cream cheese in a food processor. Scrape down the sides. Add in the eggs and sugar and pulse until incorporated. Don't over-mix or it will become too runny. Scrape the seeds from the vanilla beans and add in to cheese mix. Add in the rest of the ingredients, except the ginger, and process until smooth. Then fold in the ginger.
Pour the mix into the spring form pan with the crust. Smooth the top to remove any air bubbles. Bake at 325 for about 1 hour. The sides of the cake should brown and pull away from the sides of the pan a bit. Turn off the oven and allow the cake to cool in the oven for at least an hour. This will help avoid the top cracking. You could also allow to cool at room temperature.
Remove the cake from the pan carefully and place in the refrigerator when it is ready. Allow to cool enough to top. Then, top with the blueberry compote and serve.