Preheat oven to 425 degrees F. Slide a small baking sheet into oven to preheat as well.

Set a large skillet over medium/medium-high heat. Add 1/2 tablespoon butter, toss in Brussels sprouts, and sprinkle with sea salt and pepper. Cook 2 minutes undisturbed, stir, and cook until sprouts are tender with brown edges, about 2 minutes more. Spoon into a bowl and set aside.

In the same pan, melt another 1/2 tablespoon butter. Add the sliced garlic and scatter in mushrooms; sprinkle with sea salt and pepper. Cook undisturbed about 4 minutes, or until mushrooms are nicely browned and have started to release their water. Flip, and cook until both sides have browned, about 4 minutes more. Towards the end of cook time, sprinkle mushrooms with sherry vinegar. Remove cooked mushrooms to a bowl.

Divide remaining 2 tablespoons butter into 6 small bits.

Remove preheated baking sheet from oven, add a pat of butter to each slice of bread; set butter side down on baking sheet. Carefully pile cheese on each slice of bread, reserving a bit for the tops. Slide into oven and toast 3 minutes, or until cheese has melted. Remove from oven, pile 2 of the 4 slices with cooked sprouts and mushrooms, add a sprinkle of parsley, top with remaining slices, and add a pat of butter and a sprinkle of cheese to tops. Slide into oven and cook until bread is golden brown and cheese is bubbling – about 5 minutes more.

Serve immediately.