Preheat the oven to 425 degrees F with a rack set on the middle shelf. Heat a large cast-iron pan over medium-high heat.
Gently toss the baby turnips, potatoes and onion wedges with 2 tablespoons of the oil and a light sprinkle of salt and pepper. Carefully add to the hot pan and put in the oven to roast until the vegetables are golden brown and the potatoes are cooked through, 20 to 25 minutes.
While the vegetables are roasting, prepare the miso butter. Stir together the butter, miso, garlic, ginger and half of the scallion greens.
Thickly slice the reserved turnip greens and stems (about 1/2-inch pieces).
Remove the vegetables from the oven and turn off the heat. Gently stir in the reserved turnip greens and scallion whites until just wilted, 1 to 2 minutes. Add the miso butter to the pan and gently toss to coat the vegetables. Return to the oven to keep warm while you cook the eggs.
Heat the remaining oil in a large nonstick pan over medium heat. Crack 4 to 6 eggs into the pan; if they stick together, that's OK. Sprinkle lightly with salt and pepper. Cook until the whites start to set, 2 to 3 minutes, and then cover with a lid and continue cooking until the whites are set but the yolks are still runny, 1 to 2 minutes.
To serve, top the roasted vegetables with the fried eggs and garnish with the remaining sliced scallions.
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