01 - Place chicken, carrots, celery, onion, garlic, chicken broth, thyme, parsley, salt, and black pepper into the slow cooker. Stir gently to mix ingredients evenly.
02 - Cover and cook on low heat for 5 hours, or until the chicken and vegetables are tender.
03 - In a small saucepan, melt 2 tablespoons unsalted butter over medium heat. Stir in 3 tablespoons all-purpose flour and cook for 1 minute. Gradually whisk in heavy cream until mixture is smooth and thickened. Remove from heat.
04 - Using two forks, shred the chicken directly in the slow cooker until pieces are bite-sized.
05 - Stir the prepared cream sauce into the slow cooker with the chicken and vegetables until fully combined.
06 - In a mixing bowl, combine 1 cup all-purpose flour, baking powder, and 1/2 teaspoon salt. Cut in 2 tablespoons cold, cubed unsalted butter until the mixture resembles coarse crumbs. Stir in 1/2 cup milk just until combined; avoid overmixing.
07 - Drop tablespoon-sized portions of dumpling dough evenly over the mixture in the slow cooker.
08 - Cover and cook on high heat for an additional 45 to 60 minutes, until dumplings are fully cooked and fluffy.
09 - Taste the dish and adjust salt or pepper as desired. Serve warm.