Preheat the oven to 325°F (160°C).
In a small saucepan, heat white sugar and water over medium heat, stirring constantly until combined. Once combined, take the syrup off the heat and let it cool completely.
In a large bowl, beat the eggs and add milk. Once combined, add the syrup to the egg mixture.
To ensure a silky smooth texture, strain the egg and milk mixture through a fine mesh sieve into a bowl, removing any lumps. If you don’t have a mesh sieve, use a cheesecloth to strain the mixture or carefully use a slotted spoon to gently skim the top of the mixture and remove any lumps.
Pour the egg and milk mixture into a baking dish or ramekins.
Place the baking dish or ramekins inside a larger roasting pan. Fill the roasting pan with hot water, making sure it reaches halfway up the sides of the baking dish or ramekins.
Bake for about 45-60 minutes, or until the pudding is set (a knife inserted in the center should come out clean).
Once the pudding is baked, remove it from the oven and the water bath. Let it cool to room temperature, then refrigerate for at least 3 hours or overnight.