Preheat the oven to 400 degrees F. Lay the pastry on a floured surface and cut in half. Sprinkle one piece with the almonds and some sugar; lay the other piece on top. Press together with a rolling pin to make a 6-by-14-inch rectangle. Score a 1-inch border with a knife. Pierce the middle with a fork and make small slits with a knife. Transfer to a baking sheet lined with parchment paper, brush with water and bake until golden, 20 to 25 minutes. Cool on a rack.
Stir 3/4 cup sugar, 2 tablespoons water and the lemon juice in a heavy pan. Cover and cook over medium-high heat just until the sugar melts. Uncover and cook, swirling the pan, until amber, about 5 minutes. Remove from the heat; add the plums, 3 tablespoons butter and the vanilla pod and seeds. Cook over low heat, tossing, until the plums are soft and the sauce thickens, about 20 minutes. Add the remaining 3 tablespoons butter and swirl to combine.
Transfer the crust to a platter. Top with the plums and half of the sauce. Serve with ice cream and the remaining sauce on the side.