For the caramel, pour the water into a medium saucepan and top with the sugar. Set the pot over medium-high heat and cook without stirring until the sugar dissolves and the mixture becomes deeply golden brown, approximately nine to 11 minutes. Once the sugar starts to turn a little golden, you can gently swirl the pan but do not stir the mixture at all prior to adding the cream as this will cause crystals to form and prevent your caramel from being silky smooth.
Remove the caramel from the heat, carefully add in the cream and Irish cream, and whisk to combine. Return the caramel to the heat and cook, stirring frequently over medium-low, until the caramel has thickened. This should take approximately five minutes. Whisk in the butter and salt, cool slightly on the stove, then transfer the caramel to a container to chill completely in the fridge.
Once the caramel has cooled, place a standard loaf pan in the freezer while you prepare your ice cream base.
In a large bowl, mix the sweetened condensed milk with the vanilla extract and sea salt and set aside. In a separate bowl, combine the whipping cream and Irish cream and whip to stiff peaks. Using a whisk, fold about a cup of the whipped mixture into the condensed milk. Switching to a rubber spatula, fold in the remaining whipped cream mixture.
Retrieve the chilled loaf pan from the freezer as well as the Irish cream caramel from the fridge. Pour half of the ice cream base into the chilled loaf pan then drizzle on about 1/4 cup of the caramel. Pour over the remaining ice cream base followed by another drizzling of 1/4 cup of caramel and place it into the freezer for at least six hours to firm up.
To serve, scoop the Irish cream ice cream into dishes and pour the remaining caramel on top straight from the fridge or heated gently in the microwave.