The secret to the complex, fabulous flavor in this simple homemade butter is yogurt! Use laban or labneh, or whole milk yogurt.
In a small bowl, stir a few tablespoons of the cream into the laban, loosening it so it will more easily combine with the rest of the cream. If using thicker labneh, do this several times.
In a 4-cup measure or large bowl, combine the cream with the loosened laban. Cover loosely with a damp paper towel, and let the cream rest on the counter for at least 24 and up to 36 hours.
Chill the cream to about 60°F. It is fine to leave the cream in the refrigerator longer and it chills down more than that. Just leave it out at room temperature to warm it up to 60°F.
Using an electric mixer fitted with the whisk attachment, whip the cream all the way past whipped, until small curds of yellow butter separate from the buttermilk. Pour off the buttermilk and save for another use.
“Wash” the butter of the buttermilk by pouring about ¼ cup of ice water at a time over the butter. Use a spatula to fold the butter with the ice water, then pour off the milky liquid. Repeat this until the liquid is nearly clear.
Use your hands to knead a few large pinches of sea salt into the butter. Taste and add more salt if needed.
Lay the butter out on a sheet of parchment (or two, or three, depending on how large you want your round butter slices to be). Roll the butter with the parchment into a tight log, using a bench scraper if you have one to tighten the log by pushing the edge up against the log from the parchment side. Twist the ends and tie off with twine if you like.
Chill. To serve, cut the butter into small discs and serve at room temperature, sprinkled with more sea salt.