Sauté the Vegetables: In a large Dutch oven or heavy pot, heat the olive oil or butter over medium heat. Add the chopped onion, carrots, and celery. Cook until the vegetables are soft, about 5-7 minutes.
Add Garlic: Stir in the minced garlic and cook for 1 minute until fragrant.
Add Flour: Sprinkle the flour over the vegetables and stir well to coat. Cook for another 2 minutes, stirring frequently.
Add Broth and Seasonings: Slowly pour in the chicken broth while stirring to avoid lumps. Add the milk, bay leaf, thyme, parsley, salt, and pepper.
Add Chicken: Stir in the shredded chicken and bring the mixture to a gentle simmer. Let it cook for 10 minutes to allow the flavors to meld.
Mix Dry Ingredients: In a medium bowl, whisk together the flour, baking powder, and salt.
Add Wet Ingredients: Stir in the melted butter and milk until a soft dough forms. Be careful not to overmix.
Drop Dumplings: Drop spoonfuls of the dough into the simmering chicken stew. The dumplings should be about the size of a golf ball.
Cover and Simmer: Cover the pot and let the dumplings cook for 15 minutes. Do not lift the lid during this time, as the steam is essential for cooking the dumplings.
Check Dumplings: After 15 minutes, check that the dumplings are cooked through. They should be fluffy and no longer doughy inside.
Remove Bay Leaf: Take out the bay leaf and give the stew a final stir.
Garnish: Sprinkle with fresh parsley if desired.
Serve Hot: Ladle the Chicken and Dumplings into bowls and serve warm for the ultimate cozy meal.