Preheat oven to 400°F. Cut potatoes into 3/4- to 1-inch pieces. Peel parsnip and turnip and cut both into 3/4- to 1-inch pieces as well. Peel onions and cut into 1/2-inch segments, keeping the root end intact.
Place potatoes, parsnip, turnip, and onion in a medium bowl and top with salt and olive oil; toss to coat. Sprinkle with thyme, coriander, cumin, and paprika. Toss to coat and transfer to a baking sheet. Roast for 40 minutes or until tender. Serve warm or at room temperature.