With the rack in the middle position, preheat the oven to 150°C (300°F).
Caramel: In a saucepan, heat the sugar and water until it turns golden brown. Meanwhile, warm a Bundt pan of approximately 24-cm (3 ½-inch). Using a silicone brush, paint the interior with the caramel.
Custard: In a saucepan, heat 125 ml (1/2 cup) of sugar and the water until it turns golden brown. Remove from the heat and slowly add the cream. Reheat to ensure that the sugar is fully dissolved. Add the milk.
In a bowl, whisk by hand the eggs with 1/4 cup of sugar. Whisk in the hot egg mixture. Strain through a fine-mesh sieve. Pour the egg mixture into the Bundt pan.
Line a roasting pan with a dishtowel or other cloth. Place the Bundt pan in the roasting pan and add enough boiling water to reach halfway up the sides of the Bundt pan. Bake until just set, 1 hour 15 minutes.
Remove the Bundt pan from the oven. Let cool, then refrigerate overnight. Before serving, run the tip of a knife around the inside of the pan to facilitate unmoulding. Unmould onto a serving plate.