Place the chicken breasts in the bottom of the slow cooker.
Add the chopped onion, carrots, celery, and minced garlic on top of the chicken.
Pour in the chicken broth and sprinkle the dried thyme, dried parsley, salt, and black pepper over the ingredients.
Cover and cook on low for 4 hours, or until the chicken is cooked through and vegetables are tender.
Remove the chicken breasts from the slow cooker and shred them using two forks. Set aside.
In a medium saucepan, melt 1/4 cup unsalted butter over medium heat.
Whisk in 1/4 cup all-purpose flour and cook for 1-2 minutes until lightly golden, stirring constantly.
Gradually whisk in 1 cup whole milk and continue whisking until the mixture thickens and becomes creamy, about 3-4 minutes.
Pour the creamy mixture into the slow cooker and stir to combine with the broth and vegetables.
Return the shredded chicken to the slow cooker and stir to combine.
In a medium bowl, whisk together 1 1/2 cups all-purpose flour, baking powder, and 1/2 teaspoon salt.
Add 3/4 cup whole milk and 2 tablespoons melted butter to the flour mixture and stir until just combined to form a sticky dough.
Drop spoonfuls of the dumpling dough onto the surface of the chicken mixture in the slow cooker, spacing them evenly.
Cover and cook on high for 30 minutes, or until the dumplings are cooked through and fluffy.
Serve the chicken and dumplings hot.