Cut the mushrooms of the slices. In a medium bowl, mix vinegar, oil, basil, oregano, salt, and pepper. Pour this composition over mushrooms. Allow standing at room temperature for 15 minutes. Place a grill tray on a small fire.
Remove the mushrooms from the marinated juice and leave them on the grill for 5-8 minutes. Pour a little marinade in the meantime.
In the last two minutes, place the slices of cheese over. The composition is then placed in the burger slices.