For the pastry:
Combine the flour and salt in a large mixing bowl. Cut in the butter until the mixture resembles coarse meal. Blend in the egg, 1 tablespoon of water and the lemon juice in another bowl. Drizzle this mixture over the flour mixture and toss with a fork until the dough comes together, adding more water if necessary. Form into a ball and wrap in plastic wrap. Refrigerate for at least one hour. Dust a work surface lightly with flour. Roll three quarters of the dough (return the remaining one-fourth dough to the refrigerator for later use) out to about one-fourth-inch thick and set the dough directly on a baking sheet, pinching the edges to form a one-half-inch-high rim.
For the filling:
Toss the apples, brown sugar, flour and cinnamon in a mixing bowl to coat evenly.
To assemble:
Preheat the oven to 375 degrees. Arrange the apples in tight rows either lengthwise or crosswise on top of the dough on the baking sheet. Roll the remaining dough (from the refrigerator) out on a lightly floured surface. Using a fluted pastry cutter, cut the out into one-half-inch strips. Blend the egg and milk for a glaze. Brush this mixture on the rim of the crust. Crisscross the strips over the filling, gently pressing into the rim. Brush the strips with the remaining glaze. Bake for about 50 minutes, or until golden brown. Mix the powdered sugar, lemon juice and water and drizzle over the tart. Serve warm.