In a medium saucepan, bring the half-and-half, vanilla extract and Baileys to a simmer over medium heat.
While the liquid is heating up, place the yolks and sugar in a bowl. Vigorously whisk together.
When the cream begins to simmer, turn the heat down to low and ladle about half of the liquid into the yolks while whisking (this is known as tempering and will prevent the eggs from scrambling). Pour the yolk mixture back into the saucepan, using a spatula to scrape the bowl.
With the heat on low, stir the mixture in a figure 8 motion for several minutes until the sauce has slightly thickened. Remove from the heat and allow to cool for 5 minutes.
Pour the mixture into a container and cover with plastic wrap, gently pressing the plastic directly against the ice cream base to prevent a skin from forming. Chill until very cold (I prefer to let it chill overnight for best results).
Prepare in an ice cream maker according to the manufacturer's instructions.
Video
Notes
Every now and then I've had an ice cream base get slightly lumpy on me at the end while stirring the mixture. If that happens, don't worry. Simply pour the liquid through a fine mesh strainer before chilling and discard any solids. Recipe yields approximately 1 quart.