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 the watercress. If the asparagus are large, slice them in half and add them to the bowl. Pour the dressing over and fold gently to combine.
Season with more salt if needed, arrange on plates, and sprinkle with the chives before serving