In a blender, puree cream, eggs and yolks, vanilla extract, sugar, flour, vanilla bean paste and salt. Cover and refrigerate (3 hours).

Meanwhile, in a food processor, pulse the light rye flour, 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.

After dough is chilled, lightly dust flour on the counter, and roll out the pastry until it is about 2 inches wider than a 9-inch, deep-dish glass pie plate. Place the pastry in the pie pan and fold and cut the edges as needed to fit the pan and look pretty.

Refrigerate 30 minutes.

Preheat oven to 350° F. Line the pastry with parchment paper and fill the pie dish with pie weights.

Bake for about 30-50 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.

While the pie shell is cooling, make the caramelized apples. In a large skillet, cook the butter with the sugar over moderate heat until bubbling and caramelized (3 minutes). Add the apple slices and vanilla paste and cook, stirring occasionally, until the apples are tender and caramelized (5 minutes).

Carefully add the vinegar and simmer until the caramel is slightly thickened.

Preheat the oven to 325° F. Scatter half of the apples in the cooled shell.

Pour in the custard. Cover the crust with foil to prevent it from burning.

Bake the tart about 1 hour and 15 minutes, until the custard is golden and just set. Let cool on the toaster or a wire rack.

Spoon the remaining apples on top of the tart. I prefer this tart served chilled, but it can be served room temperature. I like a dallop of crème fraîche on top.