How to Make It
Preheat the oven to 325°. Butter eight 1 1/2-cup ramekins and coat with sugar, tapping out the excess.
In a medium saucepan, heat the milk with the vanilla bean until it just begins to simmer. In a large bowl, gently whisk the egg yolks with the whole eggs just until combined. Whisk in the 13/4 cups sugar just until blended. Gradually whisk the warm milk into the eggs, whisking constantly. Remove the vanilla bean, and using a sharp knife, scrape the seeds from the vanilla bean into the custard; discard the bean. Strain the custard, then skim off any foam.
Spread one-third of the brioche in the ramekins and top with half of the raspberries. Repeat with another third of the brioche, the remaining raspberries and a final layer of brioche. Transfer the ramekins to a large roasting pan. Pour the custard into the ramekins; press down to submerge the brioche. Let the ramekins stand for 10 minutes.
Sprinkle each diplomate with 1/2 teaspoon of sugar. Put the roasting pan in the oven and carefully add enough boiling water to the pan to reach halfway up the sides of the ramekins. Bake the diplomates for about 1 1/2 hours, or until the custard is set and the diplomates are puffed and golden.
Preheat the broiler. Carefully transfer the ramekins to a rimmed baking sheet and broil 8 inches from the heat for about 30 seconds, or until lightly browned. Serve warm or cold.