In a large Dutch oven, melt 1 tablespoon of butter over medium heat. Add chicken thighs, season with salt and pepper, and pour in the chicken broth. Add the bay leaf and dried thyme. Bring to a gentle simmer, then reduce heat to low, cover, and cook for 15-20 minutes until chicken is cooked through. Remove chicken to a cutting board to cool.

Add the remaining 4 tablespoons of butter to the broth in the pot. Add the chopped onion, carrots, and celery. Sauté for 6-8 minutes until softened. Stir in the minced garlic and cook for 1 minute until fragrant.

Sprinkle 1/4 cup of all-purpose flour over the vegetables. Stir constantly for 2 minutes to cook out the raw flour taste, forming a thick paste.

Slowly whisk the broth back into the vegetable and roux mixture until smooth. Continue cooking and stirring until the soup gently bubbles and thickens, about 5-7 minutes.

While the soup thickens, use two forks to shred the cooled chicken into bite-sized pieces. Stir the shredded chicken back into the thickened soup.

In a medium bowl, whisk together 1 ½ cups flour, 2 teaspoons baking powder, and 1 teaspoon salt. Pour in the milk and stir with a fork just until combined. Do not overmix; a lumpy batter is ideal.

Drop heaping tablespoons of the batter onto the surface of the gently simmering soup, spacing them apart. Reduce heat to low, cover the pot tightly, and let the dumplings steam for 15 minutes. Do not lift the lid.

After 15 minutes, remove the lid. Test a dumpling with a toothpick; it should come out clean. Turn off the heat. Gently stir in the heavy cream and fresh parsley. Season with additional salt and pepper to taste and serve hot.