A simple way to make graham cracker crumbs is to place about 10 whole graham crackers into the bowl of a food processor and process until finely ground.
Grate the zest from a large lemon and then cut that lemon in half and squeeze the juice out, making sure to strain any seeds.
Grease the bottom and sides of a 10-inch spring form pan. In a small skillet, heat the butter over low heat.
In a small bowl, mix the graham cracker crumbs, confectioners’ sugar, melted butter, cinnamon, and ginger, stirring until the mixture comes together. Press the crust evenly into the bottom of the prepared pan and chill while you make the filling. You can also make the crust the day before by covering it and chilling it overnight.
Preheat the oven to 350 degrees. In a mixer, using a paddle attachment if you have one, cream Ile de France goat cheese and the cream cheese until softened, using a spatula to make sure the cream cheese doesn’t get stuck inside the paddle. Gradually add the sugar and then the eggs, one at a time, beating well, until the filling is light and fluffy, about 5 minutes. Add the lemon zest and juice, vanilla, and ginger and mix another minute or two. The mixture should be light, fluffy and fully incorporated. Remove the mixture and gently stir with a spatula to make sure the lemon zest and ginger is fully incorporated and that there isn’t any cream cheese sticking to the bottom of the bowl. Place back in the mixer and mix if necessary.
Wrap the bottom of the cake pan in aluminum foil and place on a large baking sheet.
Pour the filling into the chilled crust and bake the cake on the middle shelf for about 55 minutes to 1 hour. The cake is done when it is still soft in the center; when gently jiggled, the cake should move as one.
Let cool at least one hour. Remove the outer ring of the pan and place the cake on a serving plate. Just before serving, sprinkle lightly with sifted confectioners’ sugar and surround with the berries.