Reserve two cups of the whole milk and pour the remaining milk into a large pot or double boiler. Add the beaten eggs and cook the mixture over medium-low heat, stirring often, until small bubbles begin to appear around the edges of the pot.
While the milk mixture warms, combine the sugar and cornstarch in a separate bowl. Add the reserved two cups of milk and whisk until completely smooth without any lumps.
Pour the milk-sugar mixture into the pot with the warming custard. Stir well and allow the custard to cook for another four to five minutes, stirring frequently to prevent scorching.
Check the custard for doneness by coating the back of a spoon. When you can swipe your finger across the spoon and create a line that does not fill back in immediately, the custard has thickened enough and can be removed from the heat. If you prefer to double-check the temperature, aim for around 180°F.
Stir in vanilla extract to taste. For the smoothest texture, strain the custard through a fine mesh sieve and discard any solids.
You may serve the custard warm right away, or cool it completely and transfer it to mason jars or a covered pitcher. Store it in the refrigerator until ready to enjoy.