Place the sugar and water in a heavy-bottomed saucepot over low heat. Let the sugar dissolve. Carefully brush the walls of the pot with a little water to prevent the sugar from crystallizing on the sides. Increase the heat to medium-high and boil until the syrup turns golden brown. Remove from the heat promptly and carefully divide the hot caramel among the 6 ramekins. Let cool for at least 2 minutes.
In a medium saucepan, bring the milk and cream to just below a boil over medium-high heat. Meanwhile, mix together the egg yolks, caster sugar, and vanilla in a large mixing bowl. Place the mixing bowl on top of a towel to keep it from wobbling while whisking in the hot liquid. Gently whisk 2 tablespoons of the hot milk mixture into the egg mixture. Slowly whisk in the remaining hot milk mixture 1/3 at a time, trying to prevent excess bubbles. Strain though a sieve.
Place 6 ramekins evenly spaced in a paper towel-lined baking dish to prevent the ramekins from sliding. Pour 6 ounces into each caramel-coated ramekin. Place on the extended middle rack of the oven. Carefully pour boiling water into the baking dish until 2/3 of the way up the sides of the ramekins. (Be careful not to get any water on the custard mixture.) Cover the baking dish with aluminum foil and very gently slide it towards the center of the rack. Bake for about 35 minutes, or until the custards are almost fully set. Remove from the oven. Use tongs to remove the ramekins from the hot water bath. Let stand at room temperature for 5 minutes, then refrigerate until well chilled.
To serve, dip the ramekin in very hot water for 15 to 20 seconds. Run a sharp knife around the sides of the ramekin. Invert the custards onto serving plates. The caramel will pool around the inverted custards. Serve immediately.