Coat the mushrooms with oil spray, and place directly on the grill. Grill covered for 6 minutes on one side, flip and grill on the other side for about 6 more minutes. Remove from grill when the mushrooms are tender and slightly charred. Set aside to cool.
Toss the onion and pepper with 1 tablespoon of the olive oil and salt and pepper to taste. Spread the onions and peppers into a grill pan. Place the pan on the grill alongside the mushrooms.
Stir the onions occasionally. Grill the onion mixture for 10 to 15 minutes, until the onions have browned a bit and are soft. Keep an eye on them to avoid getting them burnt up.
Start the pasta to cook according to package instructions as the vegetables grill.
When the mushrooms have cooled, chop them into bite sized pieces. Place the mushroom pieces in a large bowl, and combine with the remaining 2 tablespoons olive oil, balsamic vinegar and thyme. Stir in the grilled onions and peppers, and add salt and pepper to taste.
When the pasta is cooked to your liking, drain and toss with the mushrooms and onion mixture. Stir in the goat cheese until it has melted into the pasta. Serve and enjoy!