Fill a mixing bowl with ice and cold water and set aside.
Combine the heavy cream and sour cream in the bowl of an electric mixer fitter with the whisk attachment. Beat on high until it starts to get really thick. Add in the dill, lemon zest, salt, and pepper and continue to beat on high until the butter solidifies and separates from the liquid – from 5 to 10 minutes. (Note – things can start to splash, making a mess. Use a mixing guard or do as I do and place a kitchen towel over the mixer, taking a peek frequently so you know when it’s done.)
Gather the butter up into a ball and place in a piece of double-layered cheese cloth or a clean tea towel, squeeze gently to remove any excess liquid then rinse it in the ice water. Place in a bowl or crock and serve or refrigerate until serving time. Will last about a week.