Lightly brush a flat-bottomed rectangular container with a thin layer of neutral oil and set aside. Don’t select too large of a container, as the volume of liquid you will end up with is only about 2½ cups. (I used a small 4.5×6.5 inch/12×16 cm glass tupperware container.)
Add the whole milk, heavy cream, vanilla extract, salt, cornstarch, and sugar to a medium pot. Stir until the cornstarch is completely dissolved and there are no lumps. Then put it on the stove over medium heat.
Stir constantly with a whisk or a rubber spatula while slowly heating the milk mixture. Don’t rush it with high heat, or the texture won’t be right. During the first 3-5 minutes, stir often. Around the 6 minute mark, you’ll notice it starting to thicken and coat the spatula (pull the spatula out of the liquid periodically to check). If not, increase the heat slightly and stir until it does start to thicken. Once the thickening has begun, immediately reduce the heat to medium-low, and stir vigorously for 15-30 seconds. The milk mixture will thicken very quickly at this point, hence the minute-by-minute instructions! Remove the pot from the heat once the milk mixture is somewhere between lightly runny and pasty.
Stir off the heat until the mixture is completely smooth. Immediately transfer it to the prepared container. Cover and chill in the refrigerator overnight.
When you’re ready to fry the milk, beat the egg for a good minute until it is runny and just slightly frothy. Mix the coconut flakes and panko in a bowl. Turn the milk pudding out onto a cutting board and cut it into ½-¾ inch (about 1.5cm) thick rectangles. You can also cut it into cubes if you prefer. Set aside.
To a small pot, add just enough frying oil to submerge the fried milk. Preheat to 350°F/175°C. Dip each piece of milk pudding into the beaten egg, then coat it evenly in the panko mixture. Dropping in 3-4 pieces at a time, fry on each side for 1-2 minutes until golden brown. Repeat with the remaining pieces until you’ve fried them all. Allow to cool for a few minutes before enjoying!