Bring 4 eggs to room temperature, and separate using only the yolks.
Whip the egg yolks with the sugar until fluffy and pale yellow, set aside
In a small pot heat half and half until it is simmering, remove from the heat.
Slowly mix half of milk into the egg mixture, stirring the eggs as you pour the hot milk into them.
Add the egg mixture back into the remaining milk along with the vanilla and continue to simmer for about 5-7 minutes until the mixture has slightly thickened, use a rubber spatula to stir the mixture constantly, getting into all the corners.
When the creme anglaise looks thick enough, remove from the heat and add in the kahlua
(The Creme Anglaise should be thick enough that when you run your finger through a coating on a spoon it remains separated.)
You may strain the Creme Anglaise if it looks like it might have cooked egg in it, but if you're careful you should not need to. **
Place the pot with the finished sauce in a bowl of ice water to cool it down quickly, stirring as it cools.
Place the Creme Anglaise in the refrigerator to get completely chilled and serve with the warm bread pudding.
**do not get the creme anglaise too hot and don't be tempted to leave it on too long to try and continue to thicken. It will break and be unusable if it heats too long.