Toast the bread lightly if desired. Toast pecans or walnuts in a dry pan for 3 to 4 minutes until fragrant.
Whisk together all dressing ingredients until smooth. Season boldly with salt and pepper.
Combine shredded chicken, celery, grapes, green onions, dill, and parsley in a large bowl.
Pour dressing over the chicken mixture. Fold gently until just combined. Do not overmix.
Taste and adjust seasoning with salt, pepper, and lemon juice.
Chill for at least 15 minutes before assembling.
Butter the bread lightly. Lay lettuce on the bottom slice. Add a generous scoop of chicken salad.
Top with cucumber and avocado if using. Close the sandwich and cut diagonally to serve.