Over medium heat, bring 2 cups of the milk to a boil in a medium saucepan.

While the milk is heating, combine sugar, cornstarch, and salt in a medium, heatproof bowl. Gradually whisk in the remaining ⅔ cup of lactose-free milk. Then whisk in the egg.

Once the milk is boiling, very gradually add it to the cornstarch mixture in the bowl, whisking the whole time.

Return the mixture back to the saucepan, stirring constantly with a whisk. Once it comes to a simmer, cook it for one minute longer. Doing this will cook the cornstarch and egg fully. Large bubbles will pop at the surface and the pudding will become very thick. Remove from the heat and stir in the vanilla extract.

Strain the pudding through a fine mesh strainer to remove any lumps or pieces of cooked egg into a medium bowl. Feel free to omit this step if you do not care about little lumps in your final product.

Cover the pudding with plastic wrap, press it on the surface of the pudding, and refrigerate until chilled.

Serve with toppings once cooled.