Sauté the mushrooms in about ½ cup water until the water is evaporated. Then add a tablespoon of olive oil to the pan and add the scallions to the pan. Sauté the mushrooms and scallions, adding more olive oil as needed, stirring occasionally until the onions and mushrooms begin to brown. Remove from heat. 

Melt the butter over medium-low heat in a separate nonstick pan. Place two bread pieces in the pan and top with grated Fontina, top with mushroom and scallion mixture, and place the top slice of bread.  

Flip the sandwich when the bottom slice is golden and toasted, toast the other side. When that side is golden, remove from heat and serve.