Preheat oven to 400 degrees.
Into a small bowl, scrape seeds from vanilla bean with a knife and stir in sugar and cinnamon.
On a lightly floured surface roll out pastry about 1/8-inch thick and cut out 4 (6 by 5 1/2-inch) rectangles. Arrange pastry on baking sheet and fold edges on all sides to form a 1/2-inch border, leaving corners unfolded. Pinch corners and twist to make points. Press points down on baking sheet. With a dinner fork, gently prick middle of rectangle several times. Arrange grape halves in rows on pastry, alternating colors. Sprinkle each pastry with sugar mixture.
Bake tarts in middle of oven until pastry is golden brown, 20 to 25 minutes. While tarts are baking, in a small saucepan heat jam over low heat, stirring, until melted and strain through a sieve into a cup. On a rack cool tarts for 5 minutes and then brush with jam.
Serve tarts warm with ice cream.
Adapted from a Gourmet Magazine recipe