If cooking chicken for the salad: trim visible fat from 4 boneless chicken breasts and cut each lengthwise into thirds.
Combine 1 can chicken stock, 2 cans water, and 1–2 teaspoons Italian herb blend or poultry seasoning in a medium saucepan and bring to a boil; add the chicken, reduce heat to low, and simmer until cooked through, about 15 minutes.
Drain the cooked chicken in a colander and let it cool until easy to handle.
While the chicken cools, slice the basil leaves, wash if needed, and thinly slice the green onions; measure the grated Parmesan.
When the chicken is cool, dice it into about 3/4-inch pieces and place in a medium bowl.
Whisk together the mayonnaise and buttermilk until smooth, then stir in the sliced green onion, grated Parmesan, and sliced basil.
Pour the dressing over the diced chicken and gently toss until the chicken is evenly coated; season with salt and freshly ground black pepper to taste.
Serve immediately or chill briefly before serving.