Beat the buttermilk with your mixer. Start on low, and slowly build up to medium speed. Continue to beat until the butter separates from the buttermilk. You may find it helpful to place a towel above the mixer to avoid splattering outside of the bowl.
Remove the butter (refrigerate the buttermilk for future use if you want!) and place it into a medium-sized bowl. Place ½ cup of the ice-cold water in the bowl. Use a rubber spatula to press and move the butter around in the water. As you do this the water will turn cloudy white. Remove the water and repeat about 3-5 times until the water remains clear.
Remove the butter from the water. Squeeze butter between a clean towel or cheesecloth to remove any extra moisture.
If you are adding the salt, you can work it into the butter now either using your spoon or hands to knead it in.
Notes
Store in a covered container or parchment paper for up to a week.