In a small container, combine all dressing ingredients except the oil. Set aside.
With a mandolin or knife, slice the apple, fennel, and turnip into thin slices. If desired, cut the slices into smaller strips. Set aside.
Taste the vinegar mix and adjust. You may want more salt or more jam depending on your preference. Whisk in olive oil. Taste again and adjust seasoning.
In a large bowl, add lettuce and half of the dressing. Gently fold lettuce to coat with dressing. Once thoroughly mixed, add half of the sliced veggies and the remaining dressing. Fold again to incorporate. Add the remaining veggies and fold in again.
Top salad with pistachios and serve.