1. Bring a large pot of salted water to a boil, add the turnips and potatoes. Cook over medium heat until your roots are very tender, 20 to 30 minutes. Drain the turnips and potatoes and place them in the container of a food processor (or use a food mill or ricer).
2. Add the butter or oil and process until smooth. Taste and adjust seasoning as needed. (If youd like, cook up some orzo and mix it in with your puree for more of a main dish.)