Using a medium saucepan, add heavy cream, milk and Bailey’s; stir until well combined.

Place over medium-low heat and bring to a simmer, stirring occasionally.

Meanwhile, using a separate heat-proof bowl, whisk together the sugar and egg yolks until smooth.

Once Bailey’s mixture begins to simmer, pour half into the bowl with the eggs, whisking vigorously while you pour to prevent eggs from scrambling.

Once the custard mixture has thickened, remove from heat and add the vanilla extract; stir until well combined.

Pour mixture through a fine-mesh strainer into a clean container. Cover with plastic wrap, pressing the plastic directly onto the surface of the mixture, and refrigerate at least 4 hours, or overnight.

Once chilled, pour the mixture into an ice cream maker and churn according to the manufacturer's directions.

{Optional} When ice cream is almost done churning, add mini chocolate chips.

Transfer ice cream into a freezer-safe container and place in the freezer for at least 2 hours to harden.