Heat oven to 400°. Combine the mayonnaise, horseradish, garlic powder, rosemary, salt, and pepper; cover and refrigerate.
Toss the parsnips, oil, salt, and pepper; spread in an even layer on a baking sheet. Roast for 45 minutes, stirring halfway, until cooked through. Turn oven to broil and cook a further 5 minutes until golden and crispy. Transfer parsnips to a platter and serve with horseradish mayonnaise.