Trim both types of beets and wrap (2 per packet) in foil with a pinch of salt in each. Trim and soak turnips. If greens are nice, remove stems and rinse until clean, then spin dry. Mix with spinach and set aside. Rinse new potatoes and quarter. Toss with 2 tablespoons olive oil and 1/2 tablespoon of thyme and salt and pepper. Roast potatoes in a pan large enough for all the vegetables (except greens) at 500 degrees for 7 minutes. Toss turnips with 1 tablespoon olive oil, and salt and pepper and add to potatoes. Cook 7 minutes. Peel and trim beets and add them to potatoes with remaining thyme. Cook 3 to 4 minutes. Keep warm.
Saute spinach with 5 tablespoons oil, salt and pepper. Keep warm.
Season fillets with salt and pepper and dip in Wondra flour. Saute fillets at medium-high heat in remaining 2 tablespoons oil. When edges begin to brown, add about 1/2 tablespoon of butter. When deep golden brown (about 5 minutes), turn over using a long spatula so as not to break fillets. Saute 2 minutes more and remove. Working quickly, deglaze the pan. Add the remaining butter in 4 to 5 pieces all at once, allowing butter to foam and lightly brown. Add lemon juice, demi-glace, lemon segments, toasted bread pieces, parsley, and capers, in this order. Taste sauce for seasoning.
Arrange vegetables around top of plate and greens in center of plate. Drape skate on greens and top with sauce