Start by removing the stems from your mushrooms, brush them with a small amount of olive oil (and a dash of salt), and put on your grill. Wait until the mushrooms have begun to release their liquids, about 5 minutes. Place mushrooms on your cutting board and slice into long, thin pieces.
Arrange the bread on a work surface and brush on both sides with the garlic butter. Divide the cheese slices among the 4 slices of bread. Top two of the slices with the mushrooms and sliced shallot. Sandwich them together with the remaining bread.
Heat a grill pan over a medium-high flame and brush it with olive oil. Grill each sandwich one at a time: cook the sandwich on the first side for 2 minutes, pressing down with a spatula. Rotate the sandwich 90 degrees and cook for an additional minute. Flip the sandwich, and repeat on this side. Remove the sandwich when the cheese is properly melted, and you have nice cross-hatch grill marks on the bread.
Makes 2 sandwiches