Fill a large bowl with plenty of ice, and set aside. Find a smaller bowl that can hold finished cream.
Beat the egg yolks with a whisk or mixer for 1-2 minutes, until they're smooth.
Add the sugar and keep mixing for about 2 more minutes, until the sugar is fully mixed in and the yolks have turned to a pale yellow.
Heat the milk in a saucepan on low heat until it is not quite simmering. Don't let the temperature raise or boil. Measure the temperature with a candy/laser thermometer until it reaches 180 F.
Pour 1/4 cup of the hot milk into the egg and sugar mixture (away from the heat) while mixing constantly. The goal is to slowly raise the temperature of the egg mixture and not cook it at once. Pour another 1/4 cup repeating the process, mixing constantly to avoid cooking the eggs. Repeat this step until you've mixed the milk and egg mixture completely.
Return the custard mixture to the pot and heat at low heat, stirring constantly, until it reaches 185 F. The custard, or creme anglaise will become thick but still pourable.
Remove from heat, pour into a clean smaller bowl over the ice bath (add cold water to the ice bowl) and let cool, stirring frequently. Once at room temperature, add the vanilla extract. Wait until it is fully cooled to serve.