Place the sugar and water in a saucepan over medium heat. Cook without stirring until the sugar dissolves and turns a deep amber color.
Immediately divide the caramel among six ramekins and swirl to coat the bottoms. Set them in a roasting pan.
Make the custard:
Warm the milk and cream until steaming but not boiling. Whisk the eggs, yolks, sugar, vanilla, and salt in a bowl.
Slowly whisk the warm dairy into the eggs. Strain the custard through a fine-mesh sieve and divide among the ramekins.
Bake and chill:
Pour hot water into the roasting pan until it reaches halfway up the ramekins. Bake at 325 F (165 C) for 40 to 45 minutes, until the centers wobble gently.
Cool the ramekins in the water bath, then refrigerate for at least 3 hours. Run a thin knife around each edge and invert onto plates.
Notes
Watch the caramel closely because it can darken quickly at the end.
Straining the custard removes foam and any small bits of cooked egg.