Preheat the oven to 400F (200 C).

Prepare a 6-cup (1 1/2 l) souffle dish or charlotte mold.

Make the caramel: Place 6 tablespoons sugar in a small heavy saucepan over medium heat.

Swirl the sugar around in the pan as it dissolves.

When it turns a pale caramel color (4-5 minutes), quickly pour it into the mold, swirling to coat the bottom.

Brush the sides of the mold with melted butter.

Whisk the eggs in a small bowl until blended and set aside.

Place the milk, 3/4 cup (150 g) sugar, and vanilla bean in a medium-size heavy saucepan.

Stir and heat over medium heat until the milk is steaming and small bubbles form around the edges.

Remove from heat, cover, and let infuse for 10 minutes.

Remove the vanilla bean, rinse well, and reserve for another use.

Return the milk to medium heat.

When small bubbles have formed around the edges, add the salt and semolina, sprinkling the semolina over the milk while stirring constantly.

Continue to stir constantly as the semolina cooks (it will thicken dramatically), until it becomes like a paste (at least 10 minutes).

Remove the semolina from the heat and whisk in the eggs until thoroughly combined.

Whisk in the nutmeg and stir in the raisins.

Pour the mixture into the prepared mold.

Bake in the center of the oven until the cake is puffed and golden (45 minutes).

Remove the mold from the oven and let it cool for 10 minutes.

Unmold the cake onto a serving platter.