Boil the potatoes in their skins for 20 minutes, drain and leave to cool. Peel them. Using a cheese grater, grate them into a large mixing bowl and sprinkle with salt.
In a frying pan saute the bacon and onions. Strip the leaves off the sprigs of thyme into the pan. Add mushrooms and cook for about 5 minutes until soft. Combine with the potatoes and mix gently, taking care not to mash them too much.
Heat oil in a frying pan and add 3 or 4 spoonfuls of the mixture, See cook's note*. Using a spatula, pat the mixture into a round flat cake. Brown it over a high heat. When the bottom side is cooked flip it over. Repeat with remaining potatoes to make 6 cakes.
Put 1/2 tablespoon of butter and a slice of Gruyere on each cake and melt under a hot grill or broiler. Turn the Rosti onto a plate and serve with a green salad, if desired.
*Cook's note: We find that it's better to cook the Rosti individually. 3 or 4 spoonfuls will serve 1 person.