In the sauce, miso contributes the rich flavor that's usually provided by meat stock. While the potatoes cook on the grill, firm the tofu in the oven, and then begin preparing the sauce. Oven-firming the tofu gives it the springy texture of an uncooked chicken breast.
2 pounds peeled baking potatoes, cut into 1-inch pieces
To prepare potatoes, cut an 18 x 12-inch sheet of heavy-duty foil; lightly coat foil with cooking spray. Place potatoes and garlic in center of foil. Gather edges of foil to form a pouch; tightly seal edges. Pierce foil several times with a fork. Place pouch on grill rack; grill 30 minutes or until potatoes are tender, turning pouch occasionally.
Place potatoes and garlic in a large bowl; add milk, sour cream, butter, 3/4 teaspoon salt, and 1/2 teaspoon pepper. Mash with a potato masher to desired consistency; keep warm.
Preheat oven to 375°.
To prepare tofu, cut tofu lengthwise into 4 slices. Arrange tofu in a single layer on a foil-lined baking sheet coated with cooking spray. Lightly coat tofu with cooking spray. Bake at 375° 25 minutes or until tofu releases 3 or more tablespoons liquid. Cool slightly.
Lightly coat tofu with cooking spray; sprinkle with thyme and 1/4 teaspoon pepper. Place tofu on grill rack coated with cooking spray; grill 3 minutes on each side or until browned. Keep warm.
To prepare sauce, heat a large nonstick skillet coated with cooking spray over medium-high heat. Add shallots; sauté 1 minute. Add mushrooms; sauté 6 minutes or until moisture evaporates. Remove mushroom mixture from pan. Add wine to the pan. Bring to a boil, and cook until reduced to 3/4 cup (about 4 minutes).
Combine 1 tablespoon water and miso, stirring with a whisk. Add miso mixture, remaining water, mushroom mixture, 1/4 teaspoon salt, and 1/4 teaspoon pepper to pan. Bring to boil; cook until liquid is reduced to about 1 cup (about 4 minutes). Stir in parsley. Serve sauce with tofu and potatoes.