In a large mixing bowl, combine the shredded chicken and Caesar dressing, mixing well to ensure every strand of chicken is coated evenly. Taste and adjust seasoning with salt and freshly ground pepper as needed.
In a separate bowl, lightly toss the chopped romaine lettuce and halved cherry tomatoes with a drizzle of olive oil and a pinch of salt, ensuring they are well coated but still crisp.
Preheat a dry skillet over medium heat. Place each corn tortilla in the skillet, heating for about 30 seconds on each side until they are warm and flexible, making them easier to fold.
For assembly, lay a warm tortilla on a plate and add a generous scoop of the Caesar chicken mixture to the center of the tortilla, allowing the flavorful chicken to take the spotlight.
Top the chicken with a delightful amount of the dressed romaine and cherry tomato mixture, followed by thoughtfully arranged slices of creamy avocado. Finish with a sprinkle of grated Parmesan cheese for that extra touch of richness.
For a burst of color and flavor, garnish each taco with a sprinkle of finely chopped fresh parsley before serving.
Serve immediately while the tortillas are warm and soft, allowing everyone to enjoy the delightful combination of flavors.