Preheat the oven to 350°. Set six 6-ounce ramekins in a small roasting pan.
In a medium saucepan, combine 1 cup of the sugar with the water and bring to a boil over moderate heat, stirring, until the sugar dissolves. Cook, swirling the pan occasionally, until the syrup turns a deep amber, about 6 minutes longer. Carefully pour the hot caramel into the ramekins, tilting them to evenly coat the bottoms. Let cool.
In a medium saucepan, combine the cream with the milk and vanilla seeds. Cook over moderate heat, stirring occasionally, until bubbles appear around the edge. Remove from the heat and let stand for 5 minutes.
In a medium bowl, whisk the eggs with the egg yolks and the remaining 1/3 cup of sugar. Gradually whisk in the hot cream. Strain the custard and ladle it into the ramekins.
Pour enough hot water into the roasting pan to reach halfway up the side of the ramekins. Bake for about 40 minutes, or until the custards are set but still wobbly. Remove the ramekins from the water bath and let cool completely on a rack, then refrigerate until chilled, for at least 6 hours or for 3 days.
To unmold, run a thin knife around the edge of the custards. Set a small plate on top of each and invert. Serve cold or at room temperature.
A honeylike wine from Sauternes, or the lesser-known Monbazillac from southwest France, echoes the creamy texture of this custard.