Heat the non stick pan, sprinkle with salt and cook the tuna steak for 4-5 minutes, turning regularly to brown the steak equally. Wrap the tuna in aluminum foil and let it stand for 5 minutes.
Put the Balsamic Vinegar of Modena IGP in saucepan with sugar. Cook over low heat for 2-3 minutes, until the vinegar is reduced by 1/3 and then leave the obtained syrup to cool. Wash the thyme and parsley, dry them well and chop them roughly.
Put the chopped herbs into the saucepan with syrup, add 3 tablespoons of extra virgin olive oil, salt and pepper and beat up the sauce lightly with a whisk.
Drain the mushrooms in a thick-meshed strainer to remove oil in excess. Cut the tuna fillet into slices 2-3 cm thick. Arrange the slices in a serving dish, add the mushrooms and drizzle with the balsamic sauce.