The day before, make the turnip gratin and cook it. Let it cool and wrap tightly in foil – still in the dish – then chill overnight. Reheat (with the foil still on to prevent the top burning) at 180C/ 160C fan/gas 4 for 40 mins until piping hot.
Preheat the oven to 150C/130C fan/gas 2. Thinly slice the potatoes and turnips to about 2mm thick – you can use a Japanese mandolin if you have one – then toss together in a large bowl. Pour the cream in a pan, then add the garlic, plenty of salt and some white pepper – be generous when seasoning the cream as the potatoes and turnips aren’t seasoned separately. Bring the cream to the boil, then remove from the heat and put to one side. Grease a large gratin dish and layer a third of the potatoes and turnips in the dish, slightly overlapping each other as if you are building a wall. Pour over a third of the warm cream, then continue in this way with the remaining potatoes, turnips and cream.
Put the gratin in the oven and cook for 20 mins. Remove the dish from the oven and push the potatoes and turnips down with a fish slice. This will help to release the starches and the cream will eventually reduce and thicken. Put the gratin back in the oven and repeat the process every 10 mins until the potatoes and turnips feel tight and firm. Return to the oven for another 20 mins and cook until golden brown and tender – test by inserting a sharp knife through the potatoes and turnips. Remove from the oven and leave to cool slightly.