Instructions: Put the flour, sugar and salt in a food processor and pulse several times to mix. Remove the lid and scatter the butter pieces over the dry ingredients.

Pulse the machine repeatedly - six or seven one-second bursts - until the butter is broken into very small pieces.

Place the egg yolk in a 1 cup glass measure and add just enough water to equal 1/4 cup liquid. Using a fork, blend the water and yolk. Remove the lid of the processor and pour the liquid over the entire surface of the dry ingredients. (That is, dont pour it in only one spot.) Pulse the machine again, in short bursts, until the pastry starts to form large clumps. Tear off a sheet of plastic wrap about 14 inches long.

Empty the contents into a large mixing bowl. Using your hands, pack the dough as you would a snowball. Knead the dough two or three times, right in the bowl.

Put the dough in the center of the plastic wrap and flatten it into a disc about 3/4 inch thick. The edges probably will crack slightly; just pinch and mold them back into a smooth disc. Wrap the dough in the plastic and refrigerate until firm enough to roll, about an hour.

On a sheet of lightly floured waxed paper, roll the pastry into a 13 1/2 inch circle using a floured rolling pin. Invert the pastry over a 9 inch deep-dish pie pan. Center it, then peel off the paper. Gently tuck the pastry into the pan, without stretching it, and sculpt the edge into an upstanding ridge. Place the pie shell in the freezer for at least 30 minutes, then fully bake it.

To bake the pie shell, tear off a long sheet of aluminum foil and press it into the pastry until it fits like a second skin.

Fill the foil with about 1 1/2 pounds of dried beans, pushing them up the sides a little to keep the pastry snug in the pan.

Bake the pie shell on the center rack of a preheated 400-degree oven for 20 minutes. Remove from the oven. Using pot holders, grasp the foil on either side and slowly lift the beans out of the shell.

Using a fork, poke the bottom of the pastry five or six times, twisting the fork slightly to enlarge the holes, so steam can escape. This will prevent the pastry from puffing up.

Put the pie shell back in the oven and bake for seven to eight more minutes for a partially pre-baked shell, or bake for about 15 minutes for a fully baked shell. The bottom of the former will be a light golden in color; the latter will be a bit darker.

For the filling:
Preheat oven to 350 degrees.

Leaving the skins on, cut the apples into crosswise slices 3/4 inch thick.

Core each slice and select the six best-looking ones.

Melt the 1 1/2 tablespoons of butter in a large skillet and add the apple slices, sprinkling 1 tablespoon of the granulated sugar over them. Fry over medium heat for about four minutes, then flip the slices and fry them on the other side for a few more minutes, until nearly tender. Sprinkle the remaining 1 tablespoon granulated sugar over the apples and flip again. Cook for a minute or two longer, until the slices are tender. Transfer the slices to a plate.

Meanwhile, combine the brown sugar and flour in the bowl of a food processor.

Pulse to mix. Add the eggs and yolk and the vanilla. Process until smooth. Add the buttermilk and melted butter and process just until blended.

Put one apple ring in the center of the pre-baked pie shell and arrange the others around it. Very slowly pour the buttermilk custard over the apples. If the slices dont rise, lift them with a fork. Put the pie directly on the center oven rack and bake for about 45 minutes. To check for doneness, poke the pie pan. The custard shouldnt move in waves, but instead should seem set in the center; dont overbake. Transfer the pie to a cooling rack and let cool thoroughly. Cover with plastic wrap and refrigerate for several hours before serving.

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