Make the caramel sauceIn a small pot or pan, add the sugar and water. Heat over medium heat without stirring until the sugar melts and turns amber. Lower the heat and let it deepen to a dark brown color. Remove from heat and carefully add the hot water. (it will splatter, so be careful!) Immediately pour the caramel evenly into heat-resistant containers while hot. Set aside to cool.
Prepare the custard mixtureIn a bowl, add the eggs and gently beat until fully combined (avoid whipping in too much air). Add milk, sugar, and vanilla extract, then mix well until the sugar is completely dissolved.
Strain and pourStrain the custard mixture through a fine mesh strainer to create a smooth texture. Pour the strained mixture into the containers over the cooled caramel.
Set up for steamingCover each container loosely with aluminum foil. Place them in a steamer.Alternative method: You can also place the containers in a pot filled with hot water up to halfway up the sides of the containers. Line the bottom of the pot with a thin kitchen towel to prevent the containers from shaking and to avoid a rough texture from sudden direct heat.
Steam gentlySteam over low heat for 10–15 minutes. Check doneness by gently shaking a container. If the surface is set and the center jiggles slightly without liquid movement, it’s done. If it still looks runny, steam for another 2–3 minutes.
Rest and chillTurn off the heat and leave the lid on for 5 minutes. Remove the containers and let them cool slightly, then refrigerate for 2–3 hours until fully chilled.