Combine the ⅔ cup sugar and water in a small saucepan. Cook over medium heat, swirling, until it becomes a deep amber caramel, about 8 to 10 minutes. Immediately pour a tablespoon into each of four 6-ounce ramekins, tilting to coat the bottom.

In a blender, blend the eggs, ⅓ cup sugar, milk, cream, and vanilla on low for 30 seconds until smooth. Let the mixture sit until the foam subsides.

Strain the custard through a fine-mesh sieve, then divide it evenly over the hardened caramel.

Place the ramekins in a deep baking dish and pour hot water into the dish until it reaches halfway up the sides. Bake at 325°F (160°C) for 40 to 45 minutes, until the edges are set and the centers jiggle softly.

Cool the ramekins to room temperature, cover, and refrigerate for at least 4 hours. To serve, run a knife around the edge, invert onto a plate, and spoon the caramel sauce over the top.