Step 1: In a large Dutch oven or heavy-bottomed pot, add the chicken thighs, bay leaf, and black peppercorns. Cover with chicken broth and enough water to fully submerge the chicken. Bring to a boil over medium-high heat, then reduce heat to low, cover, and simmer for 25-30 minutes, or until the chicken is cooked through and easily shreds.
Step 2: Carefully remove the cooked chicken from the pot and set aside to cool slightly. Strain the broth through a fine-mesh sieve into a separate bowl to remove any solids. Discard the bay leaf and peppercorns. Return the strained broth to the pot.
Step 3: Once the chicken is cool enough to handle, shred it into bite-sized pieces using two forks. Discard any bones or skin. Set the shredded chicken aside.
Step 4: In a medium bowl, whisk together the all-purpose flour, baking powder, salt, and black pepper for the dumplings.
Step 5: Gradually add the milk to the dry ingredients, stirring with a fork until a shaggy dough forms. Be careful not to overmix; just combine until no dry streaks of flour remain. The dough should be soft and slightly sticky. Cover the bowl with a clean kitchen towel and let it rest for 10-15 minutes.
Step 6: Bring the strained chicken broth back to a gentle simmer over medium-low heat. Stir in the heavy cream (or half-and-half) and butter until fully melted and incorporated. Taste and adjust seasoning with additional salt and pepper if needed.
Step 7: Once the broth is simmering gently, drop the dumpling dough by rounded teaspoons directly into the hot broth. Do not overcrowd the pot; work in batches if necessary.
Step 8: Cover the pot tightly and simmer for 15-20 minutes without lifting the lid. After 15 minutes, you can quickly check one for doneness.
Step 9: Gently stir in the shredded chicken and fresh chopped parsley. Cook for another 2-3 minutes, just long enough to heat the chicken through. Serve immediately, garnished with extra fresh parsley if desired.