Bring a second pot of salted water to a boil. Add turnip greens and cook until just tender, about 5 minutes. Remove with a slotted spoon to a colander and let drain. Repeat with broccoli rabe. Reserve 1/2 cup cooking liquid. Let greens cool and then roughly chop.
In a large deep skillet, heat 4 tablespoons olive oil over medium heat. Add garlic, parsley and ground fennel. Cook, stirring constantly, until garlic begins to brown, about 30 seconds. Add turnips, greens, salt and pepper. Cook, stirring frequently, until greens are tender and begin to stick to skillet, about 10 minutes. Add some reserved cooking liquid to moisten. Turn heat to low and let stand 2 minutes. Drizzle with additional olive oil if desired. Turn greens out onto a platter to serve.