Bring milk and stock to the boil in a saucepan while stirring. Stir in polenta and parmesan. Let simmer for about 10 minutes. Season to taste with salt and pepper. Spread evenly (approx. 1 cm thick) on a greased baking tray and let it cool down for approx. 30 minutes.
Peel, wash and coarsely dice the potatoes and parsnips and cook in boiling salted water for about 20 minutes. Wash and slice the tomatoes. Cut out approx. 16 thalers from the polenta with a cutter ring (8 cm Ø).
Put the thaler on a baking tray lined with baking paper. Drain the potatoes and parsnips, add olive oil and mash with a potato masher. Season to taste with salt and nutmeg.
Spread the puree on the talers, cover with tomatoes and bake in a preheated oven (electric cooker: 175 °C/ convection oven: 150 °C/ gas: see manufacturer) for 5-6 minutes. Wash the thyme, shake dry and pluck the leaves from the stalks.
Serve polenta talers, sprinkle with thyme and coarse pepper.