Preheat the oven to 425 degrees F. Combine 2 scallion pieces, the garlic, 1/3 cup olive oil, 1/4 cup water, the herbs, walnuts, 1 tablespoon vinegar, 1/2 teaspoon salt and a few grinds of pepper in a blender; puree until smooth. Rub 3 tablespoons of the mixture all over the turkey, loosening the skin and rubbing some underneath. Set the rest aside.
Heat the remaining 2 tablespoons olive oil in a large ovenproof nonstick skillet over medium-high heat. Add the turkey, skin-side down, and cook until the skin is golden and slightly crisp, about 3 minutes. Flip the turkey and arrange the potatoes, carrots, eggplant and the remaining scallions around it. Cook until the turkey and vegetables start browning, about 2 minutes. Add 1/2 cup water and the remaining 1 tablespoon vinegar.
Transfer the skillet to the oven. Roast until the vegetables are tender and a thermometer inserted into the center of the turkey registers 165 degrees F, 20 minutes. Slice the turkey; serve with the vegetables and the remaining scallion-herb sauce. Top with pomegranate seeds.