Mix the cream and yogurt in a medium bowl and let the cream stand on the counter for 18 hours. I know, I know. It goes against everything you've learned about food safety. By setting out the cream-yogurt mixture, it develops the delicious tang, which lends the cultured butter an oh-so-marvelous flavor. Now here's the counterintuitive part: put the milk back in the refrigerator until it's fully chilled. You want cold cream to make butter.
Fill a bowl with ice and water.
Pour the cream mixture into the bowl of a stand mixer fitted with the whisk attachment. Beginning on the lowest setting, gently whisk the cream. There's no lost-to-the-ages secret in starting low. You simply sidestep getting bathed in cream until it thickens. (Don't ask me how I know.)
Gradually bump up the speed higher as the cream starts to billow. Eventually, you'll form soft peaks, them firmer peaks, then--that's it!--you're past the point of no return when you see little grains in the cream. That's the butter forming. Now, cover the mixer with a dish towel. Trust me. You don't want to bathe in buttermilk.
Let the cream go on like this until a, well, butter-yellow clomp clings to the whisk. Continue on, for a minute or two, to release as much of the buttermilk as you can.
Drop the butter, and its attendant buttermilk, into a fine-mesh screen. Let the butter drain for several minutes.
Dunk the butter into the water, and save the buttermilk for another use. Squeeze and massage the butter with your hands under the ice water to release the last little bits of buttermilk. If you're fanatical, you can dump the now-cloudy water, replenish, and repeat. About this time, you'll lose most of the feeling in your fingers due to early-stage hypothermia. (Kidding, but it's bitchin' cold.)
Remove the butter from the water and pat it dry with paper towels. If you'd like salted butter, sprinkle the butter with the salt, and knead it thoroughly.
Press the cultured butter into a crock or small bowl, cover well with plastic wrap, and refrigerate.