Peel the parsnips and halve them lengthways, then remove any large, tough cores, and cut into 1.5cm-thick batons.Boil in well-salted water for 3-4 minutes, until tender, then drain, reserving about 100ml of the cooking liquid.
Spread the parsnips in an even layer in a 25 x 25cm gratin dish. Mix together the cream, reserved parsnip cooking water, garlic, mustard, horseradish and thyme leaves, and season generously with salt and plenty of freshly ground black pepper.
Pour this over the parsnips in the dish. Place in the oven and bake for 30-35 minutes, until golden and bubbling.