Preheat the slow cooker if necessary; see the manufacturer's instructions. Spread the slices of French bread with the butter. Layer the bread in a 1.2 litre (2 pint) heatproof dish that will fit comfortably in your slow cooker pot, allowing for a gap of at least 1.5 cm (¾ inch) all the way around. Sprinkle the chopped white chocolate between the layers of bread.
Beat together the egg yolks and sugar in a bowl with a fork. Pour the cream and milk into a saucepan and bring just to the boil. Gradually stir into the egg mixture, then stir in the vanilla extract.
Pour the cream mixture over the layered bread slices and leave to stand for 10 minutes.
Cover the top of the dish with foil, then lower it into the slow cooker pot, using foil straps or a string pudding bowl lifter (see
Meanwhile, make the blueberry coulis. Purée the blueberries with the sugar and water until smooth. Pour into a jug and set aside.
Lift the dish carefully out of the slow cooker. Remove the foil and sprinkle the remaining sugar over the top of the pudding. Caramelize the sugar under a hot grill or with a cook's blowtorch. To serve, spoon the bread and butter pudding into bowls and sprinkle with extra blueberries and white chocolate. Stir the blueberry coulis and pour it around the pudding.