Place Mornay sauce in a small skillet over low heat to start warming.

Melt butter in a large skillet over medium heat. Add mushrooms, sprinkle with salt and pepper, and cook until browned. Push mushrooms to one side of the skillet and add two slices of bread with cheese on top. Scoop some of the mushrooms over the cheese, cover with remaining bread slices. Transfer remaining mushrooms to Mornay sauce.

Grill and flip sandwiches until both sides are toasted and cheese is melted, about 5 minutes per side.

To plate, place about a tablespoon of Mornay sauce in the middle of the plate, place sandwich on top, then cover with remaining sauce. Grind pepper diagonally across the top and serve immediately.