The unfamiliar greens appearing in greengrocers around the country these days can be used to spark new recipes. Don't wash shiitake mushrooms before cooking; wipe with a clean cloth or, better, a mushroom brush.
ln a shallow bowl, mix together the oils, garlic, and 2 tablespoons of vinegar. Crush the herbs gently between fingers to release flavor, and add to marinade. Add mushroom caps, and marinate for 1 hour.
Heat a grill, hibachi, or grill pan to medium heat. Lightly salt and pepper mushroom caps, and grill them gill side down for 2 to 3 minutes, until soft and lightly marked; turn and cook for 2 to 3 minutes more.
Strain marinade and add the remaining vinegar. Season to taste. Toss mixed greens and mushrooms gently with enough dressing to coat lightly, and serve.