Pour the cream into a saucepan and add the thyme and/or rosemary and some salt and black pepper. Place over a medium-high heat until bubbles begin to form around the edges of the pan, then remove from the heat.
Set aside for half an hour for the flavours to infuse, then strain through a fine sieve to remove the herbs.
Peel and slice the potatoes and the turnips/swede.
Grease a baking dish with butter. Arrange the vegetable slices in the dish in an overlapping fashion, alternating them and seasoning to taste with salt and pepper as you go.
Pour the cream mixture over the top; it should almost cover the vegetables. Gently press the turnip/swede and potato slices down using a spatula. Dot with butter and sprinkle over the grated cheese.
Bake for 40 minutes until the vegetables are tender.