Add the sugar and water to a mug and mix well. Microwave until it turns into caramel, about 2 minutes depending on your microwave's power (check after 1 minute and continue in short intervals as needed).

Coat the sides of the mug with the caramel and let it cool. Meanwhile, in another mug, beat the egg with the sugar, milk, and a splash of vanilla extract until well combined.

Strain the mixture to remove any solids, then pour it into the mug with the caramel. Microwave on medium power for 2 minutes. Check doneness by inserting a toothpick—if it needs more time, continue microwaving in 30-second intervals until set. You can unmold it while warm or let it cool in the refrigerator if you prefer.