Whisk the olive oil, vinegar, lemon zest, mustard, shallot, poppy seeds, honey, and a pinch of salt together in a small bowl.
Using a mandoline, slice the turnips and radishes into thin translucent rounds. Put them in a large bowl and add greens and carrot. Pour the dressing over and fold gently to combine
Season with more salt if needed, arrange on plates, and sprinkle with the cilantro before serving.