Place the sugar and water in a large, deep, heavy bottomed saucepan. Cook, swirling the pan (don't stir it, use a wet pastry brush to brush down any sugar crystals clinging to the sides), until the sugar has melted and turned a deep amber.
Immediately remove from the heat and pour in the hot cream (be careful - it will bubble up ferociously), wait until the bubbling has subsided then add the milk. Whisk until smooth then whisk in the salt, start with a small amount, taste, and add more as needed. Return the pan to the heat and heat until it is just starting to come up to the boil.
Meanwhile, whisk together the egg yolks and cornflour until smooth. Gradually pour the hot caramel mixture into the eggs, whisking constantly.
Return the mixture to the pan over a low heat, stir constantly until the mixture has thickened enough to coat the back of a spoon, then pour it through a fine mesh sieve into a clean bowl.
Whisk in the vanilla paste then cover the bowl and chill until it is completely cold, at least four hours.
Churn the custard in an ice cream machine according to the manufacturers directions.