Meanwhile, saute the mushroom stems with whatever veggies you like--I used additional mushrooms and some Swiss chard, along with more garlic because DELICIOUS.
Put the mushroom caps on the grill, starting gill side down. After a few minutes, flip those suckers, and lightly fill with those sauteed veggies*. Top with a few slices of good melty cheese. In this batch I had a lovely Scamorza, a smoked fresh mozzarella. Close the grill and in just a few minutes your cheese will be melted. If the mushrooms are not yet soft enough, move away from the heat.
If desired, you can garnish with something a little acidic--fresh tomatoes, capers- the possibilities are endless.
We let them sit for a few minutes and then cut into wedges like a pizza.
*Sure, you can put some sauce in here. I just don't because it doesn't help things to stay together.