Make the pastry cream: Whisk 1/2 cup milk, 1/3 cup granulated sugar, the salt, egg yolks and cornstarch in a medium bowl. Combine the remaining 1 1/2 cups milk and 1/3 cup granulated sugar with the vanilla seeds and pod in a medium saucepan; bring to a low simmer over medium heat. Slowly pour the hot milk mixture into the bowl with the yolk mixture, whisking constantly. Return to the pan and bring to a simmer, whisking; cook, whisking, until thickened, 1 more minute. Transfer to a bowl and remove the vanilla pod. Lay plastic wrap directly on the surface and refrigerate until cold, about 1 hour, 30 minutes.
Meanwhile, roast the peaches: Preheat the oven to 400 degrees F. Combine the peaches, granulated sugar, lemon juice, and vanilla seeds and pod in a medium bowl; toss gently to coat. Transfer to a rimmed baking sheet and spread in a single layer. Roast, tossing once, until tender and glossy, about 30 minutes. Let cool.
Cook the puff pastry: Coat a baking sheet with cooking spray. Unroll the puff pastry sheets on a generously floured surface and arrange them so they overlap by about 2 inches to make 1 large piece of pastry. Lightly flour a rolling pin and roll out the dough into a 17-by-12-inch rectangle. Carefully transfer the dough to the prepared baking sheet and prick all over with a fork. Bake, pricking it again halfway through, until golden and crisp, 25 to 35 minutes. Let cool completely on the baking sheet, then transfer to a cutting board and cut crosswise into 3 equal pieces.
Assemble the napoleon: Lay 1 piece of puff pastry on a platter. Spread with half of the pastry cream, then top with half of the roasted peaches. Repeat with another piece of puff pastry and the remaining pastry cream and peaches, reserving a few peach slices for topping. Top with the remaining piece of puff pastry and dust with confectioners' sugar. Top with the reserved peaches. Slice with a serrated knife.