Fill a medium pot with water and salt to taste. Add a few peppercorns, the half onion, and the chicken breasts. Bring to a simmer then cover and continue simmering on low for about 45 minutes, until the chicken is fully cooked and shreds easily with a fork.
In the meantime, make the dressing. Toast the walnuts in a skillet and set aside to cool.
In a small blender (or using an immersion blender) puree the parsley, mayo, and yogurt.
Combine the puree with all of the other ingredients except for the fresh greens in a bowl.
Strain the cooked chicken, discarding the onion and peppercorns, and move it in a bowl. When it's cool enough to touch, pull the chicken apart with your fingers or two forks. You're wanting 1-2 inch chunks. It's okay if they're not uniform! All those nooks and crannies will help the dressing stick to it.
Add the chicken to the bowl with the dressing. Roughly chop the greens and add them to the mix.
Eat fresh on a salad or, my fav, on toasted brioche buns.
Note, the greens will start to get soggy pretty quick, so this is best enjoyed immediately or the day you make it.