Heat a dutch oven or stock pot over medium heat. Add the butter and swirl to melt.
Add in the onions, celery, and carrots and saute until soft, 4-5 minutes.
Once the vegetables have softened, add in the thyme, pepper, and garlic and stir, and saute for an additional 1 minute, or just until the garlic is fragrant.
Add in the flour, stirring to coat the vegetables and absorb the fat in the pot. Cook, constantly stirring, for 2-3 minutes, or until it changes color ever so slightly. Don’t let it brown or burn, instead remove it from the heat if you feel it is cooking too quickly. Then reduce the heat and try again.
Slowly add in the broth, ½ cup at a time, and whisk until smooth before making another addition.
Once all of the broth has been incorporated, add in the cooked chicken and the heavy cream (if using). Bring to a low simmer and allow to cook for 5 minutes, whisking often, or until thickened.
Once thickened, add the peas, black pepper, and enough salt to taste. Adjust the seasonings based on your liking.
Meanwhile, the batter for the dumplings by whisking together the flour, baking powder, salt, and pepper. Then add in the parsley (if using), melted butter, and milk. Fold the wet ingredients into the dry just until combined.
Add a little more milk if needed to make a sticky, cohesive dough.
Use a heaping tablespoon or cookie scoop to drop the dumpling batter into the simmering stew. Repeat until all of the dough is used up. (I used a large cookie scoop).
Reduce the heat to low-medium, which should keep the stew at a low simmer. Cover the Dutch oven with a lid and allow the dumplings to steam for 15 minutes, or until cooked through.
Once the dumplings are cooked through, sprinkle with fresh parsley and serve immediately.