To make pastry sift flour into a bowl. Cut cold butter into small pieces with a wire cheese cutter. Add butter to flour and work it into the flour with the back of a fork. Do not use your hands or anything that would add heat to the mixture. When the butter has been worked into the flour as much as possible, add ice water, 1 tablespoon at a time and mix it in with a large spoon. It will probably only take 2 or 3 tablespoons of water to form the dough. As soon as the dough can be rolled into a ball in the bowl put it in plastic wrap and place it in the refrigerator.
When the dough has been in the refrigerator for 1/2 hour, start to coat the bottom of the pie pan. I prefer to use the deepest pie pan I can find. Spread 1 tablespoon of butter over the bottom and sides of the pie pan. Depending on the size of the pan you might have to use more or less, but I like my coating to be generous. Then sprinkle 1/3 cup of brown sugar over the butter, with a light coating covering the bottom and sides. As with the butter you may have to use more or less depending on pan size. Then place the pecan nut halves, flat side up, on the bottom and sides of the pan. I start in the middle with 1 nut and then put the rest in circles around the center, closely spaced. Finish with a layer of nuts covering the side of the pan. The entire bottom and sides should be covered with nuts. Next take the dough out of the refrigerator, cut the ball in 1/2, wrap 1/2 in the plastic wrap and put it back in the refrigerator. Roll out the other 1/2 taking care not to handle the dough too much. Place the rolled out dough in the pie pan over the pecan nut coating, and trim the edges. Cover with plastic wrap and put in the refrigerator.
Preheat the oven to 450 degrees F.
To make the filling place 1/4 cup of butter and 1 cup of sugar in a small pan and cook over medium heat. When the butter and sugar have mixed into a liquid form add 1/2 vanilla bean. Stir the mixture constantly until it starts to turn brownish, or caramelized. Then remove it from the heat. Fill a large bowl with cold water and squeeze in 1/2 of the lemon. Peel the apples, cut into thin slices and put into the bowl with cold lemon water. I like to cut the slices rather thin, 1/8-inch or so. In a small bowl mix together 1 rounded teaspoon cinnamon, 1 pinch nutmeg, and 2 tablespoons of all-purpose flour. Drain the apples in a colander and wipe all water out of the large bowl. Put the apples back in the bowl and sprinkle with the cinnamon, nutmeg and flour mixture. Mix until they are all covered.
Take the pie pan out of the refrigerator and put 1/2 on the apples over the bottom pastry layer. Squeeze 1/2 of the lemon into the caramelized butter and sugar mixture, mix and pour half of the mixture through a sieve onto the apples. Layer the other 1/2 of the apples on top of that and pour on the rest of the caramelized mix. The pie should be just slightly over filled, and formed to a dome in the middle. Remove the second half of the pastry ball from the refrigerator and roll it out. Brush the bottom lip of the pie pastry with water to help form a seal. Place the rolled pastry on top of the pie and trim with kitchen scissors. Crimp the edges together with your fingers to make a good seal between the top and bottom pastry layers. Cut 3 small slits in the top to allow steam to escape. Place pie on a cookie sheet and wrap aluminum foil around the pie edges.
Place the cookie sheet and pie in the center of the oven and allow to cook for 15 minutes. Then reduce the heat to 350 degrees F and cook for an additional 25 minutes. Remove the aluminum foil and check the crust to see if it is golden brown. You will probably have to continue to cook for another 5 to 10 minutes for the crust to turn golden brown. Remove the pie from the oven and allow it to set for 5 minutes. Then place a large plate over the top of the pie and flip it over. Gently lift the pie pan off of the pie. It should come off clean, but if any pecans stick to the pie pan remove them and put them back on the pie. Allow to cool at least 1 1/2 hours before cutting.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.