In a saucepan, bring the cream with the processed cheese, tomato paste, salt, pepper and sugar to the boil. Pour in some milk if it gets too thick. Add the frozen peas. Take off the stove.
In the meantime, cook the tortellini according to the instructions on the packet.
Cut the mushrooms into thin slices.
Put the tortellini in a baking dish, spread the mushrooms over the top. Pour the tomato-cream sauce over it, sprinkle with cheese and bake in the oven at 200 degrees for about 20 minutes.