Heat oven to 400°F. In large bowl, combine 4 cups flour and salt; mix well. With pastry blender or fork, cut in shortening until mixture resembles coarse crumbs. Add 2/3 cup water, 1 tablespoon at a time, tossing and mixing lightly with fork. Add water until dough is just moist enough to form a ball when lightly pressed together.
Shape dough into smooth ball. Divide dough into 3 pieces. On lightly floured surface, roll out 1 piece of dough as thin as possible, about 1/8 inch thick. With floured knife or pizza cutter, cut dough into 3x1-inch strips. Place strips on ungreased cookie sheet. Cover remaining 2 pieces of dough.
Bake at 400°F. for 8 minutes or until strips are lightly browned. Cool on wire rack. Reduce oven temperature to 375°F.
Meanwhile, grease 13x9-inch (3-quart) baking dish. In large bowl, combine sugar and 3 tablespoons flour; mix well. Add peaches, 1 cup water and almond extract; stir to blend. Roll out 1 piece of remaining dough in shape of baking dish to about 1//8-inch thickness. Fit pastry in bottom and up sides of greased baking dish, leaving 1-inch overhang.
Spoon half of filling into unbaked pastry shell. Top with half of butter. Scatter baked pastry strips over filling. Spoon remaining filling over pastry strips. Top with remaining butter.
Roll out remaining piece of dough in shape of baking dish to about 1/8-inch thickness. With floured knife or pizza cutter, cut into 3/4-inch-wide strips. Weave strips of crust to form a lattice top over filling. Seal and flute edge as desired.
Bake at 375°F. for 50 to 60 minutes or until crust is golden brown and filling begins to bubble. Cool on wire rack for at least 30 minutes before serving.
