Heat the oven to 150 C / 300 F. Place 4 ramekins in a deep roasting pan and set aside.

Pour the coconut milk into a medium saucepan. Add the grated ginger and heat over low heat, stirring occasionally, until steaming but not simmering - about 5 minutes. Remove from heat and let the ginger infuse for 5 more minutes.

Whisk the egg yolks, caster sugar, vanilla extract, and salt in a mixing bowl until the sugar dissolves and the mixture turns pale, about 2 minutes.

Strain the warm coconut milk through a fine-mesh sieve directly into the egg mixture, discarding the ginger solids. Whisk slowly and steadily to combine without creating foam.

Ladle the custard mixture evenly into the 4 ramekins, filling each about three-quarters full.

Place the roasting pan in the oven, then carefully pour hot water around the ramekins until it reaches halfway up their sides. Bake for 25 minutes, until the edges are just set and the center has a slight wobble when you nudge the pan.

Lift the ramekins out of the water bath using tongs or a folded dish towel. Let them cool to room temperature, then cover and refrigerate for at least 2 hours before serving.