How to Make It
In a blender, puree all of the ingredients until smooth. Transfer to a bowl, cover and refrigerate for 3 hours.
In a food processor, pulse the light rye flour with the all-purpose flour, sugar and salt to blend. Add the butter and pulse until it is the size of small peas. Drizzle in the ice water and pulse until the pastry just starts to come together. Turn the pastry out onto a work surface and gather into a ball. Flatten to a 1-inch-thick disk, wrap in plastic and refrigerate for 1 hour.
On a lightly floured work surface, using a lightly floured rolling pin, roll out the pastry 1/8 inch thick. Place a 9-inch, deep-dish glass pie plate upside down on the pastry as a template and cut out a round that is 1 1/2 inches wider than the dish. Transfer to the pie plate; fold the edge under itself and crimp decoratively. Refrigerate for 30 minutes.
Preheat the oven to 350°. Line the pastry with parchment paper and fill the pie dish with pie weights. Bake for about 1 hour and 15 minutes, until the shell is golden brown all over and cooked through. Cover the pie rim with foil if it gets too dark. Transfer the pie to a rack and let cool completely, about 1 hour.
In a large skillet, cook the butter with the sugar over moderate heat until bubbling and caramelized, about 3 minutes. Add the apple and vanilla seeds and cook, stirring occasionally, until the apples are very tender and caramelized, about 5 minutes. Carefully add the vinegar and simmer until the caramel is slightly thickened, about 3 minutes.
Preheat the oven to 325°. Scatter half of the apples in the shell. Strain the custard into a bowl and pour it into the shell. Cover the crust with foil to prevent it from burning.
Bake the tart for about 1 hour and 15 minutes, until the custard is golden and just set. Spoon the remaining caramelized apples on top. Transfer the tart to a rack and let cool to room temperature. The tart can be served at room temperature but is best chilled.