Place the quartered chicken breasts in a large pot and add the reduced-sodium 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 and is no longer pink, about 12–15 minutes.
Transfer the cooked chicken to a bowl and add a little of the cooking liquid to keep it moist while it cools.
Meanwhile, add the Greek yogurt, chopped basil, minced garlic, lemon juice, 1/2 cup roughly chopped artichoke hearts, salt, and black pepper to the small food processor and blend until smooth and creamy, scraping down the sides as needed.
Shred the cooled chicken with two forks on a cutting board until you have about 1 1/2 cups shredded chicken, then transfer it to a large bowl.
Add the yogurt dressing to the shredded chicken along with the minced sun-dried tomatoes, pine nuts, minced red onion, and Italian seasoning.
Finely chop the remaining 1/2 cup of artichoke hearts and fold them into the salad. Stir until evenly combined and adjust salt and pepper to taste.
Serve immediately or chill briefly before serving.