Place the cold whipping cream in the bowl of a stand mixer, fitted with the whisk attachment.
Whip the cream on medium–low to begin with to reduce splashing, and as it thickens, you can increase the speed to medium or even medium–high.
Whip the cream until it forms soft peaks, and then continue whipping past the point of whipped cream, where the cream becomes lumpy and the fat begins to separate. This takes about 5 minutes
Once the butterfat has separated out into clumps, whip in the ice water.
Strain the mixture through cheesecloth and a fine sieve, squeezing the butter to remove most of the water. You can rinse the butter with more ice water to make sure it's free of buttermilk.
Once you are sure you've strained away and squeezed out as much of the buttermilk and water as you can, transfer the butter to a bowl. You can use a paper towel to pat the butter and blot it to remove any moisture.
Mix in the salt.
Store the butter in the refrigerator.
Notes
You can also do this recipe with an electric mixer. You could even do this with a smaller amount of cream in a large Mason jar, close the lid, and shake the jar until the butterfat separates out. I've done it and it works. It just takes a lot of effort!This recipe yields about 25 tablespoons of butter, so 345 grams or 1.5 cups of butter, roughly.