Split the half vanilla bean and scrape out the seeds.
Place the sugar on a chopping board and mash the vanilla seeds into some of it. This way, the vanilla seeds are separated and you get "vanilla sugar."
Put cream, milk, and the vanilla bean in a saucepan over medium-high heat.
Bring it up to 70-72 degrees Celsius (158-162 degrees Fahrenheit) while stirring.
Put the sugar, egg yolks, and vanilla seeds into a bowl.
Mix the sugar into the egg yolks with a spatula.
Keep stirring the cream/milk base, so the milk doesn't burn.
When the cream base is just below the boiling point, pour half of the cream base into the egg mixture and stir it together to a homogeneous mass, so the egg base does not coagulate/separate and turn into scrambled eggs.
Pour the egg base into the pot with the cream and stir together. Continue using the spatula to mix everything together.
Now heat your creme anglaise while stirring over medium heat until the cream reaches 80-82 degrees Celsius (176-180 degrees Fahrenheit).
Stir well all over the pot so it doesn't burn at the bottom. When it (while stirring) begins to leave trails in the cream, it's almost ready. You can test if your creme anglaise is ready as follows:
Take the spatula with cream on it out of the pot and hold the spatula horizontally. Run a finger horizontally through the cream on the spatula.
So there is a strip through the cream. If the cream doesn't run, it's ready.