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.
Just as a summer dessert should be, full of fresh peach flavor. I'd stir the almonds into the peach mixture next time instead of sprinkling on tub, and use turbinado sugar on the crust for more crunch.