Preheat oven to 400F/200C or heat gas or charcoal grill to medium high. Wash mushrooms, pull out stems, and cut into halves (or quarters if the mushrooms are large.) Put mushrooms into bowl and toss with 2 T olive oil, salt, and fresh ground black pepper. Cover a roasting pan with foil, then arrange mushrooms on the pan in a single layer. (Spread them out as much as you can. For cooking on a grill, I'd probably use heavy foil to make a "pan" so the flame doesn't turn the bottom of the roasting pan black.) Roast mushrooms 15 minutes. While mushrooms cook, finely chop fresh thyme, then mix with minced garlic, balsamic vinegar, and the tsp. of olive oil. (You could mix this right in the bowl you originally tossed the mushrooms with.) After 15 minutes, drain off any liquid that has accumulated. (If you spread the mushrooms out well, the liquid will evaporate, but if yours are too crowded like mine, you'll have a little liquid to pour off.) Then toss the hot mushrooms with they garlic-thyme mixture. Arrange back on roasting pan and cook about 10 minutes more. Serve hot, sprinkled with chopped fresh parsley if desired.