Whisk egg and set aside about ¼ of it.
Put ¾ of the whisked egg and remaining dough ingredients into a food processor. Turn on the processor, run for about 10 seconds. The mixture will be crumbly, but all the flour should be incorporated. If you still see flour, pulse the motor a few times until it is all incorporated.
Knead quickly with cold hands (or in the food processor — just until it comes together as a dough). Place in a plastic bag (1 gallon zipper style is perfect) and refrigerate for at least one hour — up to 3 or 4 hours. You shouldn’t let it refrigerate overnight; the dough will be too stiff.
Peel apples, remove cores and cut apple into pieces (not too small; they should not disappear when cooked). Add lemon juice and mix. Add all other ingredients except flour and mix. Add flour and mix again.
Remove dough from the refrigerator and knead it once more, to give it a good “rolling texture.” Don’t worry if it cracks or tears; you can easily patch it. Sprinkle a clean, dry work surface with a little flour. Roll about ½ to ¾ of dough with rolling pin to about ¼ inch thick. Use it to cover the sides and bottom of a 9-inch springform pan and press it gently against the sides.
Heat oven to 350°.
Fill pastry with apples. Make thin rolls of leftover dough, flatten them (about ¼ inch thick), and weave them across the top to make a lattice topping. Brush the dough with the remaining egg.
Place the tart on a shallow baking sheet in the center of the oven and bake for 70 minutes. Turn off the heat and allow it to cool in the oven.