For the Cheddar Pastry: Combine flour, salt, butter and cheese in a food processor. Pulse until butter is the size of small peas. Transfer to a bowl, drizzle with cold water and toss with your fingertips or a rubber spatula, adding more water if needed until pastry holds its shape when squeezed between the fingers. Gather pastry together and divide into two balls, one slightly larger than the other. Flatten each into a disc, wrap in plastic wrap and chill for 30 minutes.
Preheat oven to 425°F.
Roll out larger portion of pastry on a lightly floured surface to fit an 8-inch pie plate, leaving a 1/2-inch overhang. Chill until needed. Roll out second piece for the top. Chill.
For the Filling: Combine apples, lemon juice, sugar, cinnamon and allspice in a large skillet. Cook over medium heat, stirring gently, for 5 minutes or until apples just begin to soften. Remove from heat and let stand for 5 minutes to absorb more of the syrup.
Stir in tapioca flour and heap into pie shell, mounding apples in the middle. Dot with butter. Cover with top layer of pastry, seal edges and crimp. Brush with egg wash. Cut small steam vents in top of pastry. Bake for 15 minutes. Reduce heat to 350°F and bake for another 30 to 40 minutes or until crust is golden, apples are tender and juice is bubbling. If pastry begins to brown too quickly, cover with a sheet of parchment paper.
Recipe fromThe Flavour Principle: Enticing Your Senses With Food And Drink by Lucy Waverman and Beppi Crosariol