Pour the heavy cream into the bowl of a stand mixer fitted with the whisk attachment (or use a large bowl with a hand mixer, food processor, or even a mason jar for shaking by hand).
Start mixing on low speed to avoid splashing, then gradually increase to medium-high or high speed.
Whip the cream — it will first turn into soft peaks, then stiff whipped cream, then become grainy and chunky as the fat separates. Keep going! (This usually takes 8–15 minutes in a stand mixer; longer by hand.)
You'll see the butter solids clump together and separate from the liquid (buttermilk). The mixture will look sloshy and watery once fully separated.
Stop the mixer. Pour off the buttermilk (save it for baking pancakes, biscuits, etc. — it's real cultured buttermilk!).
Add very cold water (or ice water) to the butter solids. Mix/knead gently to rinse out more buttermilk. Pour off the cloudy water. Repeat rinsing 2–3 times until the water runs mostly clear. (This step helps the butter last longer in the fridge.)
If using salt, knead it in now with a spatula or clean hands until evenly distributed.
Shape the butter into a log, ball, or press into a ramekin/butter dish. Wrap in parchment or beeswax wrap and store in the fridge for up to 2–3 weeks, or freeze for longer.