Wash the spinach and spin dry. Preheat oven (electric cooker: 225 °C/circulating air: 200 °C/gas: see manufacturer). Rub mushrooms with kitchen paper or clean and halve them with a brush. Heat oil in a pan.
Fry the mushrooms for about 3 minutes, turning them over. Add spinach. Steam covered for about 2 minutes. Season with salt and pepper.
Roll out the tarte flambée dough. On the paper, roll in about 1 cm of dough all around (see below). Press the edge lightly with possibly floured fingertips. Place the paper on a baking tray.
For the glaze, stir cream cheese with egg until smooth. Spread on the dough until the edge. Spread the spinach mushrooms on top and press down gently. Bake in a hot oven on the lowest shelf for about 15 minutes.
Slice Gouda into fine shavings with a peeler. Take the tarte flambée out of the oven. Sprinkle with cheese.