In a large bowl, combine all-purpose flour and salt. With a pastry blender or two butter knives, cut in butter/shortening until flour resembles coarse breadcrumbs.
Stir in cold water 1 tablespoon at a time until dough comes together. It is okay if there is still some loose flour. Do not overwork dough.
Divide dough into 2, one about 5/8 and the other 3/8 of the total amount of dough. Form each portion into a ball. Wrap in plastic and allow dough to rest in the fridge for 30 minutes.
Core, peel, and thinly slice all apples. In a large bowl, toss sliced apples with apple pie spice. Set aside.
Melt butter in a large saucepan. Stir in all-purpose flour and cook for 2 minutes. Add brown sugar and water and bring to a boil. Reduce heat and let simmer till mixture is thick and bubbly, about 1 to 2 minutes. Remove.
Putting it together
Roll out the larger dough ball on a lightly floured surface into a circle about 14 inches in diameter. Gently transfer dough by wrapping it round the rolling pin and unrolling it onto an 9½ inch (24cm) pie plate. Line pie plate with the dough and trim pastry to ½ inch beyond pie plate.
Arrange a layer of sliced apples on pastry lined pie plate. Spoon a third of cooked sauce onto apples. Repeat to form 3 layers.
Roll out the remaining dough ball. Cut pastry into ¾-inch (2 cm) strips. Weave strips over filling for lattice crust. Press end of strips onto the edge of pie plate. Fold bottom pastry over strips. Seal and crimp pastry.
If desired, cut out stars from the dough trimmings using a cookie cutter. Brush stars with egg wash. Sprinkle a third of the stars with paprika, a third with sesame seeds, and the final third with poppy seeds. Arrange stars on lattice decoratively.
Brush lattice with egg wash.
Bake in a 350˚F (180˚C) oven for 55 to 60 minutes.