Peel and trim the turnips to get pieces from which you can cut square slices with sides of about 7-8cm and about 0.5cm thick. A mandoline is very useful doing this but a good sharp knife is fine too. You will need four slices per portion, sixteen in all. Bring a pot of water to a boil and cook the turnips for 7 minutes. Drain the turnip slices and then transfer them to one or two oven dishes. Melt the butter, wine and stock together and pour this over the turnip slices. Season with a little salt, cover loosely with foil and place the dishes in an oven at 160C (320F). After 30 minutes, check the turnips. If they are not yet tender, continue cooking them, ensuring that they don't dry out, until they are fully cooked but not too soft to handle. The liquid should be almost all gone too.
Place the mushrooms on an oven tray, brush them with butter or olive oil, season with salt and roast them in a medium hot oven until they are tender. Chop the mushrooms coarsely and put them in a food processor with the pecans. Pulse carefully to get a coarse puree. By hand, mash or fold in the cream cheese.
Place the wine, tomato, onion, garlic, celery and cloves in a pan and bring to a boil. Simmer for 15 minutes, then blend and pass the puree through a sieve. Return the sauce to a pan and reduce by half. Season lightly with salt and pepper.
Place four slices of turnip on a parchment-lined oven tray and cover with some of the mushroom-pecan mixture. Cover each with another turnip slice, and repeat until each has four turnip layers and three mushroom. Press gently on each galette, brush the tops with a little melted butter and place the galettes in a moderate oven to heat through for 7-10 minutes.
Just before you serve the galettes, heat the reduced red wine sauce and whisk in the butter over high heat. The sauce will thicken and become a little glossy. Place a galette on each of four plates and pour the sauce around them.