Combine 1/3 cup sugar and cornstarch in a medium pot. Whisk in 1/2 cup milk until smooth. Whisk in remaining milk and cream. Bring to a boil over medium-high heat, stirring. Reduce heat to low; cook, stirring constantly, for 2 minutes.
Divide pudding into two bowls. Stir white chocolate into one bowl until melted and smooth. Stir unsweetened chocolate into other bowl until melted and smooth. Stir 1/2 tsp. vanilla into each bowl. Press plastic wrap onto surface of both puddings and refrigerate until cold, at least 2 hours and up to 1 day.
Combine berries and remaining sugar and let stand, stirring occasionally, until sugar dissolves, about 2 minutes.
Divide dark chocolate pudding among 4 1-cup glasses. Carefully divide half of white chocolate pudding over dark chocolate pudding layer. Top with raspberries, then remaining half of white chocolate pudding. Sprinkle crushed chocolate wafers on top. Serve immediately, or refrigerate, covered, for up to 2 hours.