Brush one side of each slice of bread with melted butter. Set bread aside.
Pour remaining butter into a large non-stick skillet pre-heated over medium low heat. Add onions, honey and mushrooms. Cook over medium heat, stirring occasionally until the onions begin to brown. Lower heat to low and cook for 20-25 minutes stirring occasionally until deep brown in color. Stir in port wine. Cook an additional 2-3 minutes or until wine has reduced to a glaze. Remove pan from heat and add thyme leaves. Let mixture cool.
To prepare grilled cheese, place 4 slices of buttered bread, buttered side down on a flat surface.
Place two slices of cheese over each slice of bread.
Divide cooled mushroom mixture evenly over cheese. Top each with two more slices of cheese. Place remaining bread slices on top, buttered side up. Grill each sandwich in a pre-heated skillet for 3-4 minutes over medium-low heat until golden brown. Flip sandwiches and cook an additional 2-3 minutes or until golden brown. Serve or keep warm while preparing remaining sandwiches. Repeat cooking steps with remaining sandwiches.
NOTES: Feel free to substitute button mushrooms for the shiitake and crimini mushrooms.