Prepare a medium-hot charcoal fire, or hear a gas grill for 20 minutes on high.
Brush the mushrooms, chicken, scallions and bread liberally with olive oil. Season with salt and pepper. Set aside.
Make the dressing: In a large bowl, stir together the parsley, garlic and 3 Tbs. of olive oil.
Grill the mushroom until flattened and golden brown (about 15 to 30 minutes), the chicken until streaked golden brown and springy but still moist inside (10 to 12 minutes), the scallions until slightly blackened (about 5 minutes), and the bread until golden brown, turning everything as you grill.
Meanwhile, bring large pot of well-salted water to boil and add pasta. Cook until al dente. Drain, BUT reserve about 1 cup of pasta water.
Slice the grilled mushroom and chicken thinly to about the same size as the penne; chop the scallions into 1/2-inch lengths. Crumble the toasted bread.
Add the pasta, chicken and scallions to the garlic-olive oil dressing in a large bowl and toss. Add 1/4 cup olive oil and about 1/2 cup of the reserved pasta water to moisten the pasta, using more of less water as needed.
Add the portabellas and the crumbled toasted bread. Season with salt and pepper. Serve with freshly grated Parmesan.