Preheat oven to 400 degrees. Line a rimmed baking sheet with parchment paper. Roll pie crust out to a 14-inch circle and arrange on baking sheet. Crust will overlap sides.
In the bowl of a food processor, make filling by combining almond paste, Neufchatel, sugar, egg and vanilla extract. Process until smooth, about 30 seconds, and then spread in 10-inch circle in the center of the pie crust. Arrange peach slices in concentric circles over the filling. Fold sides of crust over filling, leaving the center exposed. Spoon jam over exposed fruit. Bake tart until crust is browned and peaches are tender, about 30 minutes. Leave tart on baking sheet and allow to cool 30 minutes before serving. Serve warm or at room temperature.
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