Heat olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Add the chopped onion, carrots, and celery. Cook, stirring occasionally, until softened, about 5-7 minutes. Add the minced garlic and cook for another minute until fragrant.

Add the cubed chicken to the pot. Season generously with salt and pepper. Cook until lightly browned on all sides. You may need to do this in batches to avoid overcrowding the pot.

Pour in the chicken broth, scraping up any browned bits from the bottom of the pot. Add the dried thyme and bay leaves. Bring the mixture to a boil, then reduce the heat to low, cover, and let it simmer for 20 minutes to allow the flavors to meld.

While the stew simmers, make the dumplings. In a large bowl, whisk together the flour, baking powder, sugar, salt, and pepper. Cut in the cold butter using a pastry blender or your fingers until the mixture resembles coarse crumbs. Gradually stir in the buttermilk until a soft dough forms. Do not overmix.

Remove the bay leaves from the stew. Stir in the heavy cream and frozen peas. Bring the stew back to a gentle simmer. Drop spoonfuls of the dumpling dough (about 1-2 tablespoons each) on top of the simmering stew, leaving a little space between each one.

Cover the pot and cook for 15-20 minutes, or until the dumplings are puffed up and cooked through. Do not lift the lid while they are cooking! To check for doneness, insert a toothpick into the center of a dumpling; it should come out clean.

Gently stir in the fresh parsley. Taste and adjust seasoning with salt and pepper if needed. Serve hot and enjoy immediately.