Lightly grease a 700 ml pudding mold or round baking dish with a little butter and set aside.

Combine 80 g sugar and 1 tbsp water in a small saucepan over medium heat. Don't stir. Swirl the pan gently once the sugar starts to melt and cook until the caramel turns a deep amber color, about 4 to 5 minutes.

Pour the hot caramel immediately into the prepared mold. Tilt the mold quickly to spread caramel across the base in an even layer. Set aside to cool and harden for 5 minutes.

Whisk the fine semolina into the cold milk in a medium heavy-bottomed saucepan until combined. Add 70 g sugar and a pinch of salt.

Place the saucepan over medium heat and cook, stirring constantly with a wooden spoon, until the mixture thickens and begins to pull away from the sides of the pan, about 8 to 10 minutes.

Remove from heat. Stir in the butter pieces and vanilla extract until the butter melts completely.

Beat the 2 eggs in a mixing bowl. Add 2 large spoonfuls of the hot semolina to the eggs while whisking constantly to temper them. Pour the egg mixture back into the pan and stir well to combine.

Pour the semolina mixture over the hardened caramel in the mold. Smooth the surface with a spoon.

Leave the pudding to cool at room temperature for 15 minutes, then cover and refrigerate for at least 3 hours or overnight.

When ready to serve, run a thin knife around the edge of the mold. Place a flat serving plate face-down on top of the mold, then invert firmly. The caramel layer will sit on top as a glossy, amber glaze. Slice and serve chilled, or warm individual portions gently before plating.