Add Heavy Cream (4 cup) and Plain Yogurt (1/3 cup) into a large jar or pitcher. Whisk the mixture until it's smooth and there are no chunks of yogurt.
Cover the jar with cheesecloth and set aside for 3 to 7 days. The longer you let the cream ferment the tangy-er and more flavorful the butter will be.
When you're ready to churn the butter, chill the cream in the fridge for 1 hour. Then pour the fermented cream into a large mixing bowl, making sure to scrape all the cream into the bowl. Whisk the cream until the butter separates from the buttermilk.
Place a strainer over a clean bowl and line it with 3 layers of cheesecloth. Strain the butter and buttermilk into the cheesecloth. Twist the corners of the cheesecloth around the butter and squeeze the buttermilk out the butter. Pour the buttermilk into a clean jar and refrigerate for use in other recipes.
Add 1 cup of ice Water (1 cup) to a mixing bowl. Knead the butter in the ice water until the water turns cloudy. Dispose of the cloudy ice water and add a cup of clean ice water into the bowl. Knead the butter in the ice water and repeat this step until the water runs clear. If you plan on adding salt, you can now knead the Salt (1/2 teaspoon) into the butter at this point. Otherwise, just squeeze out as much water from the butter as possible and store in a clean container in the fridge!