Add heavy cream to the bowl of a stand mixer with the whisk attachment.
Gradually increase the speed of the mixer to high and whip until the butter and buttermilk separate. This timing depends on several different factors, but typically when I'm making butter it takes about 15-20 minutes.
You should start to notice your cream has turned into fluffy whipped cream around the 5 minute mark. At this point I will stop the mixer every 5 minutes or so to scrape down the sides of the bowl to make sure that everything gets incorporated.
Once it looks like the cream is starting to break I will place a towel over my stand mixer. As soon as the butter and buttermilk separate the liquid will splash and you will make a mess of the kitchen.
Remove the butter from the liquid (Do not throw the liquid out, this is buttermilk and can be used in other recipes). Gently press the butter between your hands until you get most of the liquid out. Removing all the excess buttermilk will help your butter stay fresher longer.
Once you have pressed as much of the buttermilk out as possible rinse in ice water.
If you want to have salted butter this is where you add it.