Preheat oven to 425 F (220 C).
Put the beets, 1 tablespoon of the olive oil, and 1/8 teaspoon salt on a sheet of aluminum foil and wrap thoroughly. Roast for about 1 hour and 30 minutes
Meanwhile, toss the apple, turnips and carrots with 2 tablespoons olive oil, 1 teaspoon salt, and the rosemary. Place on a baking sheet and roast beside the beets until browned, 15 to 20 minutes longer, and the beets are fork-tender. While warm, but not hot, rub the skin off the beets with a paper towel or clean kitchen towel. Slice the beets.
When everything is roasted, heat the remaining 1 tablespoon olive oil and the garlic in a large saute pan over medium-high until browned and fragrant. Discard the garlic. Add the beet greens and capers and saute until wilted. Add the roasted vegetables and saute until heated through. Taste for salt and adjust as needed. Remove from the heat, toss with the mustard and parsley, and set aside.
When it comes to frying the eggs, you may need to either work in batches or have two pans going at once. Heat 1 tablespoon of the butter in a nonstick saute pan over high heat. Crack 2 eggs into a small bowl and gently slide them into the butter. (If you break a yolk, discard the egg and try again.) Reduce the heat to medium and cook until the whites are set but the yolks are runny, about 2 minutes. When ready, give the pan a gentle shake to loosen the eggs.
Meanwhile, mound the roasted vegetables onto two plates. Slide the eggs on the vegetables, and sprinckle with fleur de sel. Repeat with any remaining butter and eggs.
The roasted vegetable mixture keeps, refrigerated, for up to 2 days.
"Huckleberry: Stories, Secrets, and Recipes from Our Kitchen" by Zoe Nathan © Chronicle Books 2014. Provided courtesy of Zoe Nathan. All rights reserved.