Heat the oven to 160 C / 320 F. Put a kettle of water on to boil for the water bath.

Combine the 100 g sugar and 3 tbsp water in a small saucepan over medium heat. Cook without stirring, swirling the pan occasionally, until it turns a deep amber, 6 to 8 minutes.

Pour the caramel immediately into the base of a 20 cm / 8-inch round cake pan or savarin mold. Tilt to coat the bottom, then set aside to harden.

Crush the amaretti cookies to fine crumbs using a food processor or a rolling pin over a sealed bag.

Whisk the eggs, 100 g sugar, cocoa powder and salt together in a mixing bowl until smooth and no cocoa lumps remain.

Warm the milk in a saucepan until steaming but not boiling. Whisk it into the egg mixture gradually to temper the eggs.

Stir in the crushed amaretti, rum and vanilla. Pour the custard through a fine-mesh sieve into another bowl for a smoother texture.

Pour the custard over the hardened caramel in the mold. Set the mold inside a roasting pan.

Place in the oven, then carefully pour boiling water into the roasting pan until it comes halfway up the sides of the mold.

Bake for 55 to 60 minutes, until the edges are set and the center still gives a slight jiggle. An instant-read thermometer in the middle should read about 176 F / 80 C.

Lift the mold out of the water bath and cool to room temperature. Cover and chill for at least 4 hours, ideally overnight.

Run a thin knife around the edge, place a serving plate on top, and invert. The caramel will run down the sides as a sauce. Slice and serve cold.