Chicken Satay Salad Sammies

Name: Chicken Satay Salad Sammies
Ingredients: 1 1/2 pounds thin cut chicken breast meat (cutlets); 2 tablespoons vegetable oil; Grill seasoning (recommended: Grill Mates Montreal Steak Seasoning by McCormick) or coarse salt and pepper; 3 rounded tablespoons chunky peanut butter; 3 tablespoons dark soy sauce, Tamari, eyeball it; 1/4 cup apple juice, eyeball it; 2 teaspoons hot sauce, eyeball it; 1 lime, juiced; 1/4 seedless cucumber, thinly sliced lengthwise then cut into sticks; 1 cup shredded carrots; 2 cups shredded lettuce, iceberg or hearts of romaine; 4 crusty rolls, Kaiser's or subs, split