Clean the mushrooms, wash if necessary and halve them if necessary. Peel and finely dice the onions. Pour tuna into a sieve, drain well and pluck coarsely. Stir sour cream, starch and milk until smooth.
Finely grate the cheese.
Heat the oil in a large pan one after the other. Sauté the mushrooms in it in portions for about 3 minutes. Fry the onions briefly. Season with salt and pepper. Stir in the sour-cream-mix, bring to the boil and simmer for about 2 minutes.
Add the peas and half the cheese, bring to the boil briefly. Season to taste with salt and pepper. Remove from heat.
Preheat oven (electric cooker: 175 °C/circulating air: 150 °C/gas: see manufacturer). Peel and wash the potatoes and cut them into slices about 1 cm thick. Mix potatoes and tuna with the sauce. Put everything into an ovenproof casserole dish.
Bake in a hot oven for about 1 1⁄4 hours.
Wash thyme and shake dry, remove leaves. Crumble the chips coarsely. Mix with the rest of cheese and thyme. About 15 minutes before the end of the baking time, spread the chip mix and butter in flakes on the casserole.
Finish baking, take out.