In a large bowl, mix eggnog, heavy cream, condensed milk, and vanilla. Pour into an ice cream maker, select the ice cream mode, and churn until it reaches a "soft-serve" consistency or until the process completes automatically.

Transfer the ice cream into a one- or two-quart lidded plastic container. Cover the surface with plastic wrap and seal the container. For best results, allow the ice cream to ripen in the freezer for at least 2 hours or overnight.