Bring about 600 ml of water to a boil in a saucepan. Pour rice and cook until tender for about 15-17 minutes. Throw in a colander, do not rinse. Cool.
Chop the onion into a small cube, chop the mushrooms into halves. In a small amount of vegetable oil, fry the onions until transparent, add the mushrooms and fry over high heat, stirring occasionally, until the mushrooms are rosy, for about 5 minutes. Cool.
Chop greens, grate cheese on a coarse grater. Put rice, mushrooms with onions, cheese, herbs in a bowl. Add salt and black pepper. Mix gently.
On the desktop, spread 3 - 4 layers of foil larger than the fillet. Grease one of the fillets with vegetable oil, put on a foil. Lay out the filling on top of the fish, pressing it with your hand. In the second filet on the outer surface, make cuts, trying not to cut the fish completely. Place the fillet on top of the filling and coat with vegetable oil.
Gently wrap the fish in foil layer by layer and place on a baking sheet.
Bake in an oven heated to 200 degrees for 30 minutes, then remove the fish, carefully open from the top and return to the oven for another 10 minutes, so that the top is slightly browned.
For transferring fish to a serving dish, it is convenient to use two wide shoulder blades. Pour fish over the resulting sauce if desired. When serving, garnish with fresh herbs and lemon slices.