For the crust: Preheat the oven to 350 degrees F. Generously butter the bottom and sides of a 9-inch springform pan (preferably nonstick). Wrap the outside with aluminum foil, covering the bottom and extending all the way up the side, so water will not leak into the cake as it bakes.
Place both flours, the xylitol and salt in a food processor and process for 15 seconds. Add the butter and pulse until the mixture pulls together, about 30 seconds. Add 1 tablespoon of the cream and the egg yolk. Pulse until a soft, slightly sticky dough forms. If it is still stiff, add another tablespoon of cream. Flour your fingers and gently press the dough into the bottom of the prepared springform pan until it is covered. Bake the crust just until it no longer looks moist on the top and feels set when you touch it (do not overbake), 7 to 8 minutes. Cool in the pan on a wire rack. Leave the oven on.
For the filling: Beat together 1/2 cup of the Xylitol, the arrowroot and one package of the cream cheese in a large bowl with an electric mixer (using the paddle attachment if you have it) on low about 3 minutes to make a stable starter batter. Blend in the remaining cream cheese, one package at a time, scraping down the bowl after adding each one, about another 3 minutes.
Increase the mixer speed to medium and beat in the remaining 1/2 cup xylitol. Add the eggs, beating well. The batter will look light, creamy, airy, and almost like billowy clouds. Be careful not to over mix!
Spoon the batter over the baked shortbread crust. Place the springform pan in the center of a large shallow pan and add hot water to the larger pan so that it comes about 1 inch up the side of the springform. Bake until the edge is light golden brown and the cake is light yellow beige, about 1 hour. If the center is still very jiggly, let the cake bake for 5 to 10 minutes more.
Gently remove the cake from the water bath, transfer it to a wire rack, remove the foil, and leave it on the rack for at least 2 hours and up to 4 hours. The less you move it, the less likely it is the cake will crack. Once it has cooled, leave the cake in the pan, cover loosely with plastic wrap, and refrigerate overnight until it is completely cold.
To serve, remove the springform ring from the cake and serve from the bottom of the pan (do not try to transfer it to a serving platter). Cover any leftover cake and refrigerate for up to 3 days. Do not freeze this cake.