• Place prepared mushrooms in a gallon-size freezer bag. Place garlic, vinegar, soy, and oil in a food processor; blend to make an emulsified marinade. Add marinade to mushrooms; marinate for at least fifteen minutes and up to an hour. Process gills and stems in the unwashed food processor bowl and turn into a medium saucepan; set aside.

For Grilling:

• About 20 minutes before serving, heat gas grill, igniting all burners on high for 10 minutes. When ready to grill, place mushrooms on a rimmed baking sheet and pour excess marinade into the saucepan, along with the wine and 1/4 cup water.
• Clean hot grill rack with a wire brush and lubricate it with an oil-soaked rag. Place mushrooms, cap tops down, on hot grill grate; Cover and cook until impressive grill marks form, about 5 minutes. Turn mushrooms over and continue to grill until mushrooms are cooked through, about 5 minutes longer.

For Broiling:

• About 20 minutes before serving, adjust oven rack to upper position—about 6 inches from the heating element—and turn oven to broil. Let broiler heat for 10 minutes. When ready to broil, place mushrooms, tops side up, on a foil-lined rimmed baking sheet and pour excess marinade into the saucepan, along with the wine and 1/4 cup of water.
• Broil mushrooms until impressively brown, about 8 minutes. Turn mushrooms over and carefully pour excess mushroom juice into saucepan. Continue to broil mushrooms until they are cooked through, about 5 minutes longer.

While Mushrooms Cook:

• While mushrooms grill or broil, bring sauce to a simmer over medium-high heat; continue to boil to blend flavors and reduce to a thin sauce consistency, about 5 minutes. Serve mushrooms, top sides up, with sauce drizzled over.