To make the onion jam, heat the oil and sweat the onions and thyme over a medium heat until soft and golden. Add the salt, pepper, vinegar and sugar and reduce down until a glaze. In a baking dish, add a layer of potatoes and evenly spread 1/3 of the onion jam over the potatoes. Sprinkle 1/4 of Grana Padano on top. Repeat this process 3 times using all of the onion jam and potatoes.
Top with the rest of the Grana Padano and bake in the oven for 40 minutes When ready, take out and lay the Prosciutto di San Daniele slices evenly on top. Serve immediately.