Season the mushrooms with thyme, salt, and pepper, then set aside.
Spread the garlic and herb butter on one side of each slice of sourdough bread.
Place one slice of bread, buttered side down, in a skillet over medium heat. Layer with a slice of Havarti cheese, the cooked mushrooms, another slice of cheese, and top with the second slice of bread, buttered side up.
Grill the sandwich for about 3-4 minutes on each side, or until the bread is golden brown and the cheese is melted.
Remove from heat, let it cool slightly, then slice and serve.