We started by reducing about 3 or 4 good slogs of balsamic vinegar on the stove. While that was bubbling, I whipped up a basil-and-spinach pesto (a big handful of spinach, a smaller handful of basil, and a clove of garlic--all chopped and mixed with a few slogs of olive oil, some Parmesan cheese, and salt and pepper). We basted the 'shrooms in the vinegar, and popped them on the grill (stem side down) for a few minutes. Then Sweet Husband flipped them (continuing to brush on the vinegar) and topped them each with a slice of mozzarella and a few nice spoonfuls of the pesto. Shut the grill lid for a minute or two to melt the cheese and you're done.
Sweet Husband said he thought it might be better with a little pancetta (he can't help but try to add meat sometimes), but I thought they were about perfect just as they were--and quite pretty too!