Preheat oven to 425°F; place a rimmed baking sheet in oven 5 minutes while preheating. Trim turnip stems to 1 inch. Cut trimmed turnips in half lengthwise to measure 6 cups. Chop turnip greens to measure 4 cups. (Reserve remaining turnips and greens for another use.)

Toss together halved turnips, 2 tablespoons of the oil, 3⁄4 teaspoon of the salt, and 1⁄2 teaspoon of the pepper in a bowl; spread in one even layer on warmed baking sheet. Roast in preheated oven until tender and golden brown, about 18 minutes.

While turnips roast, place 2 quarts water in a large saucepan, and bring to a boil over high. Add chopped greens; cook about 30 seconds. Fill a large bowl with ice water. Drain boiled greens, submerge in ice water, and stir once. Let stand until cold, about 1 minute. Remove greens, and squeeze out excess water. Transfer to a food processor.

Add pecans and garlic to the greens in the food processor, and process until a paste forms, stopping to scrape down sides as needed, about 1 minute. With processor running, pour lemon juice and remaining 1⁄4 cup oil through food chute in a steady stream, processing until smooth, about 1 minute. Add Parmesan, honey, and remaining 1⁄2 teaspoon salt and 1⁄4 teaspoon pepper, and process until blended, about 10 seconds. Set pesto aside until ready to serve.

Transfer roasted turnips to a serving platter; drizzle with pesto.