In a large pot or Dutch oven, heat olive oil over medium heat. Season chicken thighs with salt and pepper. Brown chicken on all sides, then remove from pot and set aside.
Add chicken broth, onion, carrots, and celery to the pot. Bring to a boil, then reduce heat and simmer for 10 minutes.
Add potatoes to the pot and continue to simmer for another 10 minutes, or until potatoes are tender.
Return chicken to the pot. Bring to a simmer.
In a medium bowl, whisk together flour, baking powder, and salt. Add milk and eggs, and stir until just combined. Do not overmix.
Drop spoonfuls of dumpling batter into the simmering broth. Cover and cook for 15-20 minutes, or until dumplings are cooked through.
Stir in frozen peas during the last 5 minutes of cooking.
Serve hot and garnish with parsley, if desired.