Place bread cubes on shallow trays. Let stand to dry out slightly while making salad.
Heat gas or charcoal grill. Place bell peppers on grill over medium-high heat.Cover grill; cook 15 to 30 minutes, turning occasionally, until peppers are blackened. Place roasted peppers in large bowl; cover with plastic wrap. Let stand 15 to 20 minutes. Peel and seed bell peppers. Cut into bite-size strips.
Place onion slices on grill. Cover grill; cook 3 to 6 minutes, turning once during grilling, until golden on edges and slightly tender. Cut into 1/2-inch pieces.
In large bowl, place cubed bread, grilled pepper strips, grilled onions, olives, basil, cheese, tomatoes and cucumber. Drizzle with dressing, tossing to coat. Serve immediately.