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For the grilled portion: - Preheat grill to medium-high heat. Meanwhile, combine all the sauce ingredients into a small saucepan. Stir over medium heat, bringing to a boil and thickened. Remove from heat. Brush half of the sauce onto the chicken breasts, reserve 2 teaspoons for the Caesar salad dressing and the rest for basting the chicken.
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Lightly oil the grill grate, and place chicken, pineapple wedges and asparagus on the grill. Cook pineapples and asparagus for 2-3 minutes per side, or until grill marks appear. Remove and cut into slices. Cook chicken for 6 to 7 minutes per side and brush with sauce 2-3 times. Chicken is done when the meat is firm, and juices run clear. Remove, allow to cool slightly, and cut into strips. Brush with the remainder of sauce.
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Make the dressing - While the chicken is cooking, make the Caesar Dressing: In a bowl, combine the Greek yogurt, lemon juice, olive oil, reserved 2 teaspoons teriyaki sauce, anchovy paste, mustard, Worcestershire sauce and garlic and whisk together until smooth. Stir in cheese and add salt and pepper to taste. (Can make ahead the night before and store covered in the fridge).
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To assemble - Just before serving, add all of the salad ingredients to a large bowl. Drizzle in the desired amount of salad dressing, add croutons and gently toss to combine. Top with grilled chicken, more Parmesan cheese, and chopped parsley, if desired.