In a small sauce pot over medium heat, melt together the sugar and water. Keep an eye on this mixture but do not stir! Let it boil until a syrup forms and begins to turn a light caramel brown color. Depending on your stove this should take anywhere from 7-15 minutes, just keep an eye for the color change.
When you have a light caramel colored syrup, remove from the heat and stir in the butter. The caramel will bubble up and steam so be careful!
After the butter is mixed in, add in the heavy cream and Irish Cream. This will bubble up again but keep stirring until everything is combined.
The mixture will be very hot so allow it to cool before using then store in a plastic or glass container. This can be stored for several weeks in the refrigerator!
To reheat for easy pouring, heat up some water in a pot until it is warm to the touch. Float your container of caramel in the warm water for a few minutes until it is soft and pourable. Make sure the lid is water tight!