Combine 2 cups sugar, flour, and nutmeg in a large Dutch oven; add peaches, and set aside 15 minutes. Bring peach mixture to a boil. Reduce heat; cook over low heat, stirring occasionally, 10 minutes or until peaches are tender and mixture thickens. Remove from heat; add almond extract and butter. Stir gently until butter melts. Set aside.
Roll one-third of pastry to 1/8- inch thickness on a lightly floured surface; cut into 3/4-inchwide strips, and place on an ungreased baking sheet. Bake at 425° for 10 to 12 minutes or until golden brown. Cool completely, and set aside.
Roll half of remaining pastry to 1/8-inch thickness; fit into a 12- x 8- x 2-inch baking dish.
Spoon half of peach mixture into pastry shell; arrange cooked pastry strips evenly over filling. Spoon remaining peach mixture over pastry strips.
Roll remaining pastry to 1/8- inch thickness; cut into 3/4-inch wide strips, and arrange in a lattice fashion over filling. Trim edges; seal and flute. Sprinkle remaining sugar on lattice strips.
Bake at 475° for 15 minutes. Reduce temperature to 375°, and bake an additional 20 minutes.