This caramel sauce can be made well in advance, and in fact will keep for a few months as well, to enjoy on all your favorite desserts.
Add the sugar and water to a medium (ideally heavy-bottom) saucepan, and place over medium heat. It will look like a small volume in the saucepan, but you want some room for the caramel to bubble up and grow in volume.
Cook the ingredients, stirring occasionally, until the sugar has fully dissolved, and the mix starts to bubble; this should take 3-5 minutes.
From here don't stir, just let the mix cook down. You may swirl the saucepan, or brush down the sides with water occasionally to help prevent crystallization and keep the cooking even.
Cook the sugar down until it thickens, and becomes a dark amber. Watch this closely, becuase a good caramel can quickly turn to burnt caramel if you're not careful. The cooking process can take anywhere from 8-12 minutes.
Once a good color is reached, add the butter a few chunks at a time, whisking to combine, adding more once the previous butter has completely melted.
Once all the butter has been added, melted, and fully mixed in, promptly remove from the heat, and slowly stream in the heavy cream while whisking constantly. Once the heavy cream has been fully incorporated, do the same with the Baileys. Last, whisk in the vanilla and optionally the salt if you want a more salted caramel flavor.
Let the caramel cool in the saucepan for about 10 minutes, and then transfer to a heat-safe glass container. Allow this to cool completely before transfering to the fridge for long-term storage (3 weeks in the fridge, 2 months in the freezer!). To serve from refrigerated or frozen, reheat in the microwave until the desired consistency is reached.