Beat evaporated milk, whole milk, Irish cream liqueur, sweetened condensed milk, brown sugar, white sugar, eggs, cinnamon, nutmeg, and salt together in a large bowl using an electric mixer; transfer to a large pot.
Slice vanilla bean down the middle and scrape seeds into the milk mixture. Place vanilla bean pod into the mixture and stir. Bring milk mixture to a boil and cook, stirring constantly, until thickened, 2 to 3 minutes. Remove pot from heat and cool to room temperature.
Fill a blender halfway with milk mixture and blend until smooth, about 15 seconds. Repeat with remaining milk mixture. Transfer milk mixture to a storage container and refrigerate until cold, 2 hours to overnight.
Pour milk mixture into an ice cream machine and freeze according to manufacturer's instructions.