Stir together first 3 ingredients and 1/4 cup basil. Set aside.
Combine mushroom caps and Italian dressing in a heavy-duty zip-top plastic bag, turning to coat. Let stand 2 to 3 minutes. Remove mushrooms from marinade, discarding marinade.
Coat food rack with vegetable cooking spray; place on grill over medium-high heat (350° to 400°).
Place mushroom caps, stem side up, on rack, and grill, covered with grill lid, 3 to 4 minutes on each side. Turn caps, stem side up, and spoon sauce mixture evenly into each.
Grill, covered, 2 more minutes or until thoroughly heated. Sprinkle evenly with shredded cheese and remaining 1/4 cup chopped basil; serve immediately.
Note: For testing purposes only, we used Classico Tomato-Basil Pasta Sauce.
Grilled Portobello Pizza Burgers: Serve Grilled Portobello Pizzas on warm, toasted hamburger buns with desired toppings.