Preheat the oven to 375 Fahrenheit. Place mushroom caps gill side down on a broiler pan and sweat in the oven for ten minutes, until they exude most of their liquid. Blot mushrooms with paper towels to remove excess liquid. Turn mushrooms over and transfer to a clean baking sheet.

Heat olive oil in a small skillet over medium high heat. Add finely chopped mushroom stems, portobello and onion. Cook until soft, about four minutes. Add the garlic, tomato tapenade, basil, parsley and thyme. Cook about three more minutes. Pour in sherry and scrape up any brown bits on the bottom of the pan, cook off alcohol, about two minutes. Remove from heat and season with salt and pepper. Fold in the parmesan cheese and mix until evenly distributed.

Use a small spoon to divide the mixture among all the mushroom caps. Bake for 15 to 17 minutes, until mushrooms are soft and stuffing is brown.