Place ¾ cup sugar and water in a saucepan over low heat. Once sugar dissolves, increase the heat to high and let the mixture bubble. The sugar mixture slowly turn golden. Do not stir the mixture. When the color turns brown, divide it among 6, 1-cup capacity ramekins. The mixture will harden in few minutes.
Preheat oven to 180C or 350F.
Place eggs, ½ cup sugar and vanilla extract in a large bowl. Whisk to combine. Set aside.
Meanwhile, place milk in a saucepan over medium-high heat. When hot, add it to milk mixture. Whisk to combine. Pass it through a sieve and pour onto the caramelized sugar layer.
Cover the ramekins with aluminum foil and place in a deep baking dish. Fill the baking dish with boiling water, halfway up the sides of the ramekins.
Transfer to oven and bake for about 30-35 minutes or until the pudding is slightly jiggly and a skewer inserted into the center of the pudding comes out clean.
Remove from oven and cool to room temperature. Chill in refrigerator for 3-4 hours or overnight if possible.
Before serving, run a knife around the edges of the pudding and flip it on to a plate.