Preheat oven to 375°.
Lightly spoon 2 cups flour into dry measuring cups; level with a knife. Place flour, sugar, and salt in a food processor; pulse 2 to 3 times. Add butter pieces; pulse 10 times or until the mixture resembles coarse meal. With processor on, slowly add ice water through food chute, processing just until combined (do not form a ball).
Gently press dough into a 4-inch circle. Slightly overlap 2 lengths of plastic wrap on a slightly damp surface. Place dough on plastic wrap; cover with 2 additional lengths of overlapping plastic wrap. Roll dough, still covered, into a 15 x 13-inch rectangle. Place in freezer 5 minutes or until plastic wrap can be easily removed; remove top sheets. Fit dough, uncovered side down, into a 2-quart baking dish coated with cooking spray, allowing dough to extend over edges ; remove remaining plastic wrap.
Combine peaches, 1/2 cup brown sugar, 2 1/2 tablespoons flour, vanilla, and cinnamon in a large bowl; toss gently. Spoon into prepared dish; fold edges of dough over peach mixture. Sprinkle 1/4 cup brown sugar over mixture; sprinkle with almonds.
Combine egg and water in a small bowl. Brush egg mixture over dough; sprinkle with granulated sugar. Bake at 375° for 45 minutes or until filling is bubbly and crust is lightly browned. Let stand 30 minutes before serving.