Place the mushrooms in a large, plastic resealable bag.
In a bowl, mix the wine, olive oil, garlic, rosemary, salt and pepper; pour over the mushrooms, press the air out of the bag and seal tightly; turn the bag to distribute the ingredients; let marinate at room temperature for 1-2 hours, turning the bag occasionally.
Grill the bell peppers over direct medium heat until they are black and blistered all over, 12-15 minutes, turning occasionally; place the peppers in a medium bowl and cover with plastic to trap the steam; set aside for at least 10 minutes, then peel the skins from the peppers and discard the stems and seeds.
Drain excess marinade from the mushrooms and grill them over direct medium heat until tender, 8-10 minutes, turning occasionally; lightly brush or spray the slices of bread on both sides with olive oil; grill until lightly toasted, 1-2 minutes, turning once halfway through grilling time.
Put the pine nuts in a medium pan over medium heat and cook until lightly toasted, 5-10 minutes, shaking the pan occasionally.
Very finely chop the bell peppers, mushrooms, and pine nuts and combine all of them in a medium bowl; add the basil and stir, taste and add salt and pepper if necessary.
Spread a very thin layer of goat cheese on one side of each slice of toasted bread; arrange about 1 tablespoon of mushroom mixture on top of each; serve at room temperature.