Put the caster sugar in a saucepan and place it over a medium heat. When it starts to melt all around the edges, give the pan a shake, leaving it on the heat. Continue to cook, shaking now and then, until the melted sugar turns to the colour of dark runny honey. This should take 5-10 minutes. Quickly pour it into the dish, tipping it around to coat the base and sides evenly.
Pour the milk into another pan and leave it to heat gently while you whisk together the eggs, sugar and vanilla extract in a large bowl. When the milk is hot, pour it onto the egg and sugar mixture, whisking until thoroughly blended. Then pour the liquid through a sieve into the caramel lined dish and place it in a roasting tin.
Transfer the tin carefully to the oven, then pour boiling water into it to surround the dish up to two-thirds in depth. Bake for 20-25 minutes or until the custard is set, then remove it from the roasting tin. When it's completely cold, cover with cling film and chill for several hours in the fridge.
When ready to serve, remove the crème caramel from the fridge then loosen it around the sides with a palette knife and invert onto a serving plate.