Preheat oven to 375°F (190°C) and butter a 2 1/2-quart oval gratin dish or 9x13-inch baking dish.

In a small saucepan, bring heavy cream and thyme sprigs to just under a boil.

Remove from heat and let stand for 30 minutes to infuse the cream with the thyme flavor.

Strain the cream through a fine sieve, discarding the thyme sprigs.

Arrange potato and turnip slices in the prepared baking dish, alternating between the two.

Season each layer with salt and pepper as you arrange the slices.

Dot the top layer with unsalted butter, if desired.

Pour the infused cream over the vegetables, ensuring it almost covers them. Add up to 1/2 cup more cream if needed.

Cover the dish tightly with parchment-lined foil.

Bake for 45 minutes, or until the vegetables are tender.

Remove the foil and bake for an additional 15 minutes, or until the top is golden brown and bubbling.

Serve immediately.