Season chicken with salt and pepper on both sides. In a large Dutch oven, heat olive oil over medium-high heat. Cook the chicken for 3-4 minutes per side until fully cooked. Remove, let cool, then dice into small pieces.
In the same Dutch oven, melt butter over medium heat. Add onion, carrot, and celery; cook until softened, about 4 minutes. Add garlic; cook for 30 seconds.
Sprinkle flour over the vegetables, stirring for 2 minutes. Add chicken stock, heavy cream, Italian seasoning, and bay leaves.
Bring to a boil, then simmer over medium heat for 5 minutes or until thickened into a gravy.
Add the diced chicken and frozen peas to the Dutch oven. Stir well and cover, reducing heat to low as you prepare the dumplings.
Make Dumplings: In a medium bowl, mix flour, baking powder, salt, sugar, pepper, and garlic powder. Pour in milk, sour cream, and melted butter, stirring just until blended. Be careful not to overmix the batter.
With the stew at a very gentle simmer, use a small (2 teaspoon size) cookie scoop to drop dumpling dough into the stew. Cover with a lid and cook for 12-15 minutes. Do not uncover during cooking to ensure proper steaming.
Remove from heat, uncover and sprinkle with chopped parsley before serving.