Pulse first 5 ingredients in a food processor until the mixture resembles coarse meal. Beat egg in a small bowl, add half of it to the dough, pulsing until it comes together and forms a ball. You may need to add a teaspoon or two more of the beaten egg. If you don't have a food processor, combine first 4 ingredients in a large bowl and cut in the butter with a pastry blender until it resembles coarse meal. Beat egg in a small bowl, and add half of it to the dough, mixing until it forms a ball.
Lay dough on plastic film or a beeswax wrap, cover with another layer of the same and press into a disc shape about 6 - 8 inches in diameter. Wrap tightlly and refrigerate the dough for at least an hour or overnight.
When you're ready to bake, preheat the oven to 350°F. and remove the dough disc from the fridge. Using a rolling pin between two sheets of parchment paper, form a disc about 12 inches in diameter. Remove the top sheet of parchment paper, invert a 9-inch round glass pie plate on top of the dough, then hold on to the bottom sheet of parchment paper and carefully flip it over so the pastry is now in the pie dish. The pastry will probably break, (expect it to) but you can easily press it back into shape. Use your fingertips to crimp the edges. Using a fork, prick the bottom and sides of the crust at half-inch intervals. Put the parchment paper back on top of the crust and fill the cavity with pie weights.
Once your oven is at temperature, bake the crust for 10 minutes, then remove the parchment paper and pie weights and bake for 5 minutes more.
Filling and Crumble Topping
Preheat oven to 375°F. Slice apples thinly and place in a large bowl. Add lemon juice and vanilla extract and toss to coat. Add tapioca flour, sugar and spices and toss.
Fill chilled pie crust with apple slices. Dot with cubes of butter.
Combine topping ingredients and press on top of apples, covering completely.
Cover edges of pie crust with a pie shield or with strips of aluminum foil to prevent excess browning.
Bake at 350°F. for 45 minutes or until apples are tender and mixture is bubbling up. Check at 30 minutes to make sure topping isn't browning too quickly.
Remove from oven and cool before slicing. Serve with ice cream, if desired.