In large bowl, stir together plums, 1/2 cup sugar, the plum preserves, vanilla and allspice. Let stand 30 minutes, stirring occasionally.
Heat oven to 425°F. Line cookie sheet with cooking parchment paper; spray paper with cooking spray. Unroll pie crust on cookie sheet; roll into 12-inch round.
Drain plum mixture, reserving liquid. In same bowl, toss plums with flour. Mound plums in center of crust, leaving 3-inch border. Fold crust up and over plums, pleating as you go. In small bowl, beat egg and water. Brush crust with egg mixture; sprinkle with 1 tablespoon sugar.
Bake 25 minutes or until filling is bubbly and crust is golden. Cool on cooling rack 15 minutes before serving. Meanwhile, in 1-quart saucepan, heat reserved plum liquid to boiling over medium heat. Boil 1 to 2 minutes or until slightly thickened. Cool slightly. Brush 1 to 2 tablespoons plum syrup over exposed fruit in center of tart. Serve immediately with remaining plum syrup.