Preheat oven to 400 degrees F. Combine apples, 2 tablespoons flour, 2 tablespoons sugar, and cinnamon in a large bowl; toss to combine. Set aside.
Combine the remaining 3 1/2 cups flour and 1/2 cup superfine sugar in a large mixing bowl. Add butter and quickly work the butter into the flour mixture using your fingertips or a pastry blender until it resembles coarse meal. Combine egg yolk and 4 teaspoons cold water; mix to combine. Divide the dough in half.
Working quickly, press 1/2 of the dough into and up over the edge of a 9-inch glass pie plate. Fill with the apple mixture, mounding in the center.
Roll remaining dough between 2 large pieces of plastic wrap into a 14-inch circle. Remove top piece of plastic wrap, and invert onto apples. Remove remaining plastic. Trim edges and decoratively crimp using your fingers. Brush lightly with 1 tablespoon water and egg mnixture, and sprinkle with the remaining 2 teaspoons sugar. With a sharp knife, cut slits into pastry. Transfer to oven and bake until golden brown, about 1 hour.