Preheat the oven to 160C/140C Fan/Gas 3. Lightly grease 6 x 150ml/5fl oz heatproof ramekins with butter. Break the egg yolks into a large bowl, tip in the caster sugar and vanilla, and mix with a wire whisk to combine.
Put both the creams in a medium pan and heat until scalding. Remove from the heat and stir in the coffee until it dissolves, then leave the mixture to cool slightly for about 2 minutes. Pour the cream mixture into the egg yolk mixture and stir thoroughly to combine. Strain the custard and pour it into the prepared ramekins.
Stand the ramekins in a roasting tin and pour hot water into the tin until it comes halfway up the sides of the ramekins. Bake for 25-30 minutes, then remove the ramekins from the roasting tin and leave to cool. Cover and chill in the fridge overnight (or up to 2 days ahead).
Put the caster sugar for the caramel in a stainless steel pan and add water to dampen. Place over a medium heat and stir until the sugar has dissolved (CAUTION: boiling sugar is very hot. Take care not to burn yourself). Once dissolved, turn the heat up high and cook until the caramel has turned a very pale straw colour. Pour the caramel onto non-stick paper, and allow to cool completely. Once cool, blitz the caramel in a food processor until very fine. Sprinkle the caramel sugar evenly over the cooled custard.
Preheat the grill to high. Put the ramekins as close to the grill as possible and grill for about 4-5 minutes. Be careful not to burn the sugar or grill for too long otherwise you will overcook the softly set custard.
If you have a chef's blowtorch you can skip steps 4 and 5, and instead add 1 teaspoon caster sugar in a layer on top of each crème brûlée and caramelise it under a direct flame.