Preheat the oven to 375˚ F, and line a baking sheet with foil or parchment paper.
Twist the mushroom stems to remove them, or use a paring knife. Reserve for another use. Gently scrape the dark gills with the tip of a paring knife to remove as many as possible without damaging the mushrooms. They hold a lot of moisture. Turn the mushrooms upside down and gently tap, to allow the scrapings to fall out. Gently rub each mushroom with a towel to remove any dirt and debris.
Whisk together the balsamic vinegar, oil, salt, and pepper in a large bowl. Carefully toss the mushrooms in the dressing to completely coat, and place them upright on the prepared baking sheet. Bake for 30 minutes, turning the mushrooms upside down halfway through.
Miso Mashed Potatoes
Place the potatoes in a medium pot and cover with well-salted water. Simmer for 25 minutes, or until tender. Peel them when they’re cool enough to handle. Slice into thick slabs.
Either mash or rice the potatoes using a potato ricer. Add the butter and miso and thoroughly mash. Stir in the chopped shallot, Half & Half, salt, and pepper.
Scoop 1 tablespoon of miso potatoes into each mushroom cap (or whatever amount makes sense for the size of the caps). Keep warm in the oven on a low temperature, or in a warming drawer until serving.
Sprinkle a few chives over the tops of each appetizer just before serving.