Prepare vinaigrette: Combine all vinaigrette ingredients in a lidded jar. Shake well just before using.
Lay clean mushrooms in a shallow baking dish and pour 1/2 cup of vinaigrette over it.
Cover and marinate for up to 24 hours, turning the mushrooms once. When ready to cook, drain dressing; reserve for another purpose.
TO GRILL: Place on grill over warm coals for 5 to 10 minutes, turning once.
TO BROIL: Place on a baking sheet and set under broiler for 5 to 8 minutes.
TO BAKE: Place baking dish in preheated 425 F oven for about 15 minutes.
NOTE: You may substitute sliced portabellas. However, you may need to grill them on a piece of foil to avoid breakage. Poke holes in the foil to assure a good smoky flavor.