Cook the Chicken: In a large pot or Dutch oven, heat olive oil over medium-high heat. Add chicken pieces and cook until browned on all sides, about 5-7 minutes. Remove the chicken from the pot and set aside.

Sauté the Vegetables: In the same pot, add diced onion, garlic, carrots, and celery. Sauté for 5-6 minutes until softened.

Add Broth and Seasonings: Pour in the chicken broth and bring the mixture to a simmer. Stir in salt, pepper, thyme, and parsley. Let it simmer for 10-15 minutes, allowing the flavors to combine.

Make the Dumpling Batter: In a medium bowl, whisk together the Bisquick mix, milk, and egg until smooth. The batter should be thick, like pancake batter.

Return Chicken to Pot: Add the cooked chicken back into the pot. Stir to combine with the broth and vegetables.

Add Dumplings: Drop spoonfuls of the dumpling batter onto the simmering broth. Be sure to cover the surface evenly. Do not stir once the dumplings are added.

Simmer and Cook the Dumplings: Cover the pot with a tight-fitting lid and allow the dumplings to cook for 15-20 minutes, until they are fluffy and fully cooked through.

Serve: Once the dumplings are done, serve the chicken and dumplings hot, garnished with fresh parsley, if desired.