In the bowl of a stand mixer fitted with the paddle attachment, mix together the sugar and butter. Mix on low speed until well blended and then increase the speed to medium and beat for another 3 minutes. Add the salt, vanilla, and cream and beat on medium for 1 minute, adding more cream if needed.
Transfer to an airtight container and store in the fridge for up to a week or in the freezer for up to 3 months. Let come to room temperature and re-whip in the stand mixer until light and fluffy again. Add a tablespoon or 2 of powdered sugar if it needs to thicken.