Pat the chicken thighs dry and season generously with salt and pepper. Heat olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Sear the chicken for 3-4 minutes per side, until golden brown. It does not need to be cooked through. Remove the chicken and set aside.

Add the butter to the pot. Once melted, add the diced onion, carrots, and celery. Cook, stirring occasionally, for 6-8 minutes, until softened. Add the minced garlic and cook for another minute until fragrant.

Sprinkle the flour over the vegetables and stir constantly for 1-2 minutes to cook out the raw flour taste. This roux will thicken our stew beautifully.

Slowly whisk in the chicken broth, making sure to scrape up any browned bits from the bottom of the pot. Bring the mixture to a simmer, then return the seared chicken to the pot.

Reduce the heat to low, cover, and let it simmer for 20-25 minutes, or until the chicken is cooked through and tender. Remove the chicken to a plate and shred it using two forks, then return the shredded chicken to the stew. Stir in the heavy cream and frozen peas. Season with salt and pepper to taste.

In a medium bowl, whisk together the flour, baking powder, salt, and pepper. In a separate small bowl, whisk together the buttermilk and melted butter. Pour the wet ingredients into the dry ingredients and stir with a fork until just combined. Do not overmix! The dough should be sticky.

Bring the stew back to a gentle simmer over medium-low heat. Drop rounded tablespoons of the dumpling dough on top of the simmering stew, leaving a little space between each one.

Cover the pot with a tight-fitting lid, reduce the heat to low, and let the dumplings steam for 15-20 minutes. Do not lift the lid while they are cooking! The trapped steam is essential for light, fluffy dumplings.

The dumplings are done when they are puffed and a toothpick inserted into the center comes out clean. Serve your homemade Chicken and Dumplings immediately, garnished with fresh parsley.