Buy a wide loaf of bakery bread for the base of this sandwich. Cutting the bread diagonally yields a surface area large enough for the topping.
To prepare bell peppers, wrap wood chips in a double layer of foil; pierce foil packet several times. Add foil packet to grill rack; grill 10 minutes. Place bell peppers on a grill rack coated with cooking spray; cover and grill 15 minutes or until blackened, turning occasionally. Place in a zip-top plastic bag; seal. Let stand 15 minutes. Peel and cut into strips. Combine bell peppers, basil, 1/4 teaspoon salt, and black pepper.
To prepare crostini, coat both sides of bread with cooking spray. Place on grill rack; grill 30 seconds on each side until lightly browned. Remove from grill; rub each bread slice with garlic clove.
To prepare sauce, combine cheese, half-and-half, and 1/8 teaspoon salt in a small microwave-safe bowl; microwave at high 25 seconds; stir well with a whisk.
Top each crostino with about 1/3 cup bell peppers; drizzle each with about 1 tablespoon sauce.