In a medium saucepan, stir heavy cream, milk, and salt over medium heat until it starts to simmer. Remove from heat.

In a medium bowl, whisk the egg yolks and sugar until smooth and pale yellow color.

While whisking egg yolk mixture constantly, gradually add hot cream mixture. Return to saucepan to low heat. Stir the mixture slowly, but constantly, scraping the bottom and sides of the pot until the base is thick enough to coat the back of a spoon. Remove from heat. (Do not let the mixture boil or you will end up with egg curdles)

Let the mixture cool completely. Add vanilla extract and Baileys.

Cover the mixture and refrigerate for at least 4 hours or up to overnight.

Transfer the churned ice cream to a freezer container. Freeze for least 4 hours before serving.