Warm the olive oil in a large heavy-bottomed pot or Dutch oven over medium heat.

Season the chicken thighs with half of the salt and half of the black pepper, then add them to the pot and cook, stirring occasionally, until lightly browned on the outside, about 5–7 minutes. The chicken does not need to be fully cooked through at this stage. Transfer the browned chicken to a plate and set aside.

In the same pot, add the diced onion, sliced carrots, and sliced celery. Cook over medium heat, stirring occasionally, until the vegetables begin to soften, about 5–6 minutes.

Stir in the minced garlic and cook for 30 seconds, just until fragrant, being careful not to let it brown.

Sprinkle the 1/4 cup of all-purpose flour over the vegetables and stir well to coat. Cook the flour for 1–2 minutes, stirring constantly, to remove the raw flour taste.

Gradually pour in the chicken broth while stirring, making sure to scrape up any browned bits from the bottom of the pot. Stir until the mixture is smooth and no visible lumps of flour remain.

Add the whole milk, dried thyme, dried parsley, bay leaf, and the remaining salt and black pepper. Stir to combine, then return the browned chicken and any juices on the plate back into the pot.

Bring the mixture to a gentle boil over medium-high heat, then reduce the heat to low, cover the pot with a lid, and let it simmer for about 15 minutes, stirring once or twice, until the chicken is cooked through and the vegetables are tender.

While the soup simmers, prepare the dumpling dough. In a medium bowl, whisk together the 2 cups of all-purpose flour (for dumplings), baking powder, salt (for dumplings), and black pepper (for dumplings).

Pour in the melted unsalted butter and the 1 cup of whole milk (for dumplings). Stir gently with a spoon until a soft, thick dough forms. Do not overmix; stop as soon as there are no dry patches of flour.

Remove the lid from the pot and discard the bay leaf. Stir in the frozen peas and bring the mixture back to a gentle simmer over medium-low heat.

Using a tablespoon or small cookie scoop, drop spoonfuls of the dumpling dough directly onto the surface of the simmering liquid, spacing them slightly apart so they have room to puff up.

Once all the dumpling dough has been added, cover the pot with the lid, reduce the heat to low, and let the dumplings cook undisturbed for 15 minutes. Avoid lifting the lid during this time so the dumplings can steam properly.

After 15 minutes, remove the lid and check that the dumplings are cooked through; they should be puffed, firm on top, and not doughy in the center. Taste the broth and adjust seasoning with a little extra salt or black pepper if needed.

Ladle the Homemade Chicken and Dumplings into bowls, making sure each serving gets a good mix of chicken, vegetables, broth, and dumplings. Sprinkle with fresh parsley for serving if you like, and serve hot.