Cut each sheet of phyllo pastry in half lengthwise to make two 17- x 6-inch sheets. Lay 1 half on work surface, keeping remaining phyllo covered with damp towel to prevent drying out. Brush sheet with butter; top with another sheet so edges are not perfectly aligned and all 8 corners are visible. Repeat with remaining phyllo and butter.
Gently fit into 14- x 4-inch tart pan with removable bottom. Turn edges under and ruffle, allowing some to hang over edge. Line with foil; fill with pie weights or dried beans. Bake in 375°F oven for 10 minutes; lift out foil with weights. Prick bottom of shell all over. Bake until golden, about 5 minutes longer. Let cool completely on rack. Remove from pan and place on serving plate.
Spread about two-thirds of the white chocolate over crust. (Make-ahead: Set aside for up to 2 hours. Remelt reserved white chocolate if necessary.) Arrange 1 cup of the raspberries over chocolate. Beat together mascarpone, cream, sugar and vanilla; spread over raspberries. Arrange remaining raspberries over filling. Drizzle with remaining chocolate.