For the Chicken:
2 cups low-sodium chicken broth, divided
1 medium yellow onion, finely chopped
3 medium carrots, peeled and diced
2 medium stalks celery, diced
2 cloves garlic, minced
4 sprigs fresh thyme
2 bay leaves
2 1/2 teaspoons kosher salt, divided
1 1/2 pounds boneless, skinless chicken thighs
1/4 teaspoon freshly ground black pepper
1/2 cup heavy cream
1/3 cup all-purpose flour
1 cup peas
1/4 cup coarsely chopped fresh parsley leaves
For the Dumplings:
1 cup all-purpose flour
1 1/2 teaspoons baking powder
1 teaspoon granulated sugar
1/2 teaspoon kosher salt
1/2 cup heavy cream
2 tablespoons unsalted butter, melted and cooled slightly
Make the Chicken:
Lightly coat the insert of a 6-quart or larger slow cooker with cooking spray. Add 1 1/2 cups of the broth, onion, carrots, celery, garlic, thyme, bay leaves, and 1 teaspoon of the salt and stir to combine.
Season the chicken all over with the remaining 1 teaspoon salt and pepper and place in an even layer in the slow cooker.
Cover and cook until the vegetables are tender and the chicken is cooked through, about 5 hours on the LOW setting.
Transfer the chicken to a large plate and cover the slow cooker again. Using 2 forks, shred the chicken into bite-sized pieces. Whisk the remaining 1/2 cup broth, cream, and flour together in a small bowl until the flour is dissolved. Add the shredded chicken, cream mixture, peas, and parsley to the slow cooker and stir to combine. Taste and season with salt and pepper as needed. Cover and continue cooking while you form the dumplings.
Make the Dumplings:
Place the flour, baking powder, sugar, and salt in a medium bowl and whisk to combine. Add the cream and butter and stir until the flour mixture is moistened and a soft dough forms.
Evenly drop the dough in heaping tablespoons onto the chicken mixture. Cover and cook until the dumplings are cooked through and the tops are no longer sticky, about 1 1/2 hours. Uncover and let stand 15 minutes for sauce to thicken slightly before serving.