Whisk together marinade ingredients. Put half of mushroom caps and half of marinade in each of 2 large sealable plastic bags, arranging mushroom caps in 1 layer, and seal bags, pressing out excess air. Marinate mushrooms at room temperature, turning bags over several times, at least 1 and up to 2 hours.
Make Gorgonzola butter while mushrooms are marinating: On a plate with a fork mash Gorgonzola and butter together until blended well. Make red pepper vinaigrette: In a blender blend vinaigrette ingredients with salt and pepper, to taste, until smooth and emulsified.
Grill 1 side of bread on a rack set 5 to 6 inches over glowing coals until golden, about 1 minute. (Alternatively, bread may be grilled in a hot well-seasoned ridged grill pan over moderately high heat.) Divide bread, toasted sides down, among 4 plates. Spread soft side of bread with Gorgonzola butter. Remove mushrooms from marinade and grill 2 to 3 minutes on each side, or until tender. (Alternatively, mushrooms may be grilled in a hot well-seasoned ridged grill pan over moderately high heat.) Transfer mushrooms with tongs to a cutting board and slice thin. Arrange warm mushrooms on toasts and spoon vinaigrette over each open-faced sandwich. Garnish sandwiches with thyme.
To roast peppers: Using a long-handled fork char peppers over an open flame, turning, until skins are blackened, 2 to 3 minutes. (Or broil peppers on rack of a broiler pan under a preheated broiler about 2 inches from heat, turning every 5 minutes, until skins are blistered and charred, 15 to 25 minutes.) Transfer peppers to a bowl and let stand, covered, until cool enough to handle. Keeping peppers whole, peel them, starting at blossom end. Cut off tops and discard seeds and ribs. (Wear rubber gloves when handling chilies.)