In the bowl of a food processor fitted with a metal blade, combine the flour, sugar, and baking powder. Cut in the butter. Pulse until butter is well distributed and the mixture resembles a coarse meal. Add eggs and pulse again until dough clumps together. Gather the dough into a ball. Divide dough and wrap in waxed paper. Chill for 1 hour.
Add water and vinegar to a medium pot. Add cherries and cook until cherries are soft. Drain.
Heat up grill.
Butter a 10-inch round cake pan. Roll dough into a circle and transfer to cake pan. Pinch edges to form a crust, like that of a pan pizza. Fill dough with pastry cream. Spread cherry preserves and cherries. Place pie on pizza on pizza stone on grill. Cook until dough is crispy and brown, about 1 hour.
In a 2-quart saucepan, combine the milk and vanilla bean and bring to a boil. Turn off heat immediately and keep warm while you whisk the yolks.
In a medium bowl, combine the yolks, sugar, and cornstarch and whisk until thoroughly combined. While whisking, slowly add the warm milk mixture into the yolks and then transfer this back into the saucepan over medium heat.
Whisk constantly while you bring the custard to a boil; it should begin to thicken immediately. Whisk until thickened completely, about 3 minutes.
Pour through a fine-mesh strainer into a clean bowl and use a rubber spatula to push everything through. Place a sheet of plastic wrap directly on the surface of the custard to prevent a skin from forming and refrigerate until completely chilled.