In a saucepan, bring together sugar and water, let cook over medium-low heat until sugar dissolve and it turns in to brown and amber-colored liquid. Add in 25g hot water, off heat and mix well. Be careful of the splash. Pour the caramel into the heatproof pudding cups. Form a thin layer of caramel in the bottom of the cups. Let set in the fridge to cool until set.
In a clean bowl, bring together 2 eggs, 1 egg yolk and sugar, mix well and set aside.
In a saucepan, bring together milk, heavy cream, vanilla extract and let cook over medium heat until simmer. Off heat, pour the liquid into the mixture while using a whisk quickly mixing them together. Sift twice.
Fill each pudding cup half full with the pudding liquid.
In a clean bowl, separate the eggs. Keep the egg white cool in the fridge.
In a clean bowl, mix well vegetable oil and milk. Add in cake flour and mix well. Add 2 egg yolks, mix well and set aside.
Add lemon juice, vanilla extract and sugar into the egg white. Use a hand mixer to beat until soft peaks form. Take a scoop of whipped egg white and gently fold it into the batter until just combined. Pour all the batter back into the whipped egg white and gently fold it in until just combined.
Fill the pudding cups with batter, smooth it out, place them in the baking tray, add in enough hot water for water-bath baking. Send into the oven and let bake for 30 minutes, then set the heat to 140℃/284℉and let bake for 20 minutes. Let cool in the fridge for 30 minutes.
