Place the quartered chicken breasts in a large pot and add the chicken broth, water, and bay leaves so the chicken is covered by about 1 inch of liquid.
Bring to a gentle simmer over medium-high heat, then reduce to medium and cook until the chicken reaches 165°F (about 12–15 minutes) and is no longer pink inside.
Transfer the cooked chicken to a bowl and reserve a small amount of the cooking liquid; add a little liquid to the bowl to keep the chicken moist while it cools.
Meanwhile, in a small food processor combine the Greek yogurt, packed basil, minced garlic, lemon juice, 1/2 cup roughly chopped artichoke hearts, salt, and black pepper and blend until smooth and creamy, scraping down the sides as needed.
When the chicken is cool enough to handle, place it on a cutting board and shred with two forks until you have about 1 1/2 cups shredded chicken.
In a large bowl toss the shredded chicken with the yogurt mixture, minced sun-dried tomatoes, pine nuts, minced red onion, Italian seasoning, and the remaining 1/2 cup finely chopped artichoke hearts until well combined.
Taste and adjust salt and pepper as needed, then serve.