Yesterday we had bagna cauda at a friend's house. It was too much, so everyone went home with a leftovers bottle (around 1 liter).
Will it ruin if I freeze it?
You can freeze cream, but it will undergo some separation issues. When you thaw it you can shake or mix it to reintegrate the milk solids that have separated. Unfortunately, it will not regain the same mouth feel as never frozen liquid dairy. Basically I never freeze dairy that I want to drink, only things I will be cooking with or baking with.
In the case of this dip, I assume it will be reheated when you want to eat it, so I would say that you can freeze it and when you reheat spend some time with a whisk to recombine fully.
Isn't bagna cauda oil, anchovies, and butter. I would say yes to freezing but whisk once back to room temperature and don't be surprised if texture changes.
I freeze it in an ice cube tray then zip lock the cubes in a bag. Then for a quick snack I put one or two cubes into a microwavable coffee cup, warm it up and dip bread into the hot mixture. Works great!