1Heat gas or charcoal grill. Between pieces of plastic wrap or waxed paper, place each chicken breast smooth side down; gently pound with flat side of meat mallet or rolling pin until about 1/4 inch thick. Sprinkle with 1/4 teaspoon of the seasoned salt and the pepper.
2In medium bowl, toss onion and mushrooms with remaining 1/4 teaspoon seasoned salt and the oil until vegetables are coated. Place vegetables in grill basket (grill “wok”).
3Place chicken and grill basket on grill over medium heat. Cover grill; cook 10 to 15 minutes, occasionally turning and brushing chicken with 2 tablespoons of the mustard-mayonnaise sauce and shaking grill basket to mix vegetables, until chicken is no longer pink in center and vegetables are tender. Add bread slices to grill for last 4 minutes of cooking, turning once, until crisp.
4Top each cooked chicken breast with vegetables and cheese slice. Cover grill; cook until cheese is melted. Spread one side of bread slices with remaining mustard-mayonnaise sauce. Top each bread slice with chicken breast.