To make dressing, whisk olive oil and sea salt into lemon juice until mixture gets creamy and emulsified.
Heat a medium-sized skillet over medium heat. Melt butter or ghee and add shallots. Cook 2 minutes, stirring a bit. Turn heat to low and cook 20 minutes more, stirring occasionally.
Meanwhile, trim greens from turnips and radishes and set aside. Slice turnips and radishes paper thin, very carefully using either a sharp knife or mandoline. Toss turnip and radish slices with a pinch or two of sea salt and two tablespoons of the vinaigrette. Set aside.
The turnip and radish greens will likely be sandy, so submerge them in a sink of water to get sand out, and then wash and spin as normal. Tear into pieces and set in a big bowl. For my salad, I used only a bit of the radish greens –– taste yours and then add them according to your preference. Sprinkle a pinch of sea salt on greens, drizzle in enough vinaigrette to lightly coat the leaves, and toss with your hands.
To serve, toss greens with turnips, radishes, and any accumulated juices. Top with warm shallots and minced chives; finish with a pinch of sea salt and pepper to taste. Serve right away.