Bring a large pot of generously salted water to a boil. Cook pasta al dente per package directions. Drain and rinse under cold water to stop cooking and cool completely. Spread on a large plate or baking sheet to cool fully.

Season chicken breasts with salt and pepper. Grill over medium-high heat for 6 to 8 minutes per side until internal temperature reaches 165 degrees F. Rest 5 minutes on a cutting board then slice into thin strips.

Whisk together olive oil, fresh lemon juice, minced garlic, salt, and black pepper in a small bowl until fully emulsified. Taste and adjust seasoning before adding to the salad.

In a large mixing bowl, combine cooled pasta, sliced chicken, halved cherry tomatoes, and torn basil. Dice avocados now and add them on top.

Pour dressing over the salad and gently fold to combine using a large spoon or spatula. Use folding motions to keep avocado pieces intact. Taste and adjust with extra lemon juice or salt if needed. Top with grated Parmesan if using and serve immediately or refrigerate.