Sweat the aromatics: In a large, heavy pot or Dutch oven, heat butter and olive oil over medium heat.
Add onion, carrots, and celery. Cook 5 to 7 minutes, stirring often, until softened. Add garlic and cook 30 seconds.
Season and simmer: Stir in salt, pepper, thyme, and bay leaf.
Pour in chicken broth and bring to a gentle boil.
Add the chicken: Reduce heat to a simmer and add chicken pieces. Cook 10 to 12 minutes until the chicken is just cooked through. Skim any foam if needed.
Thicken the base: Stir in the cornstarch slurry and simmer 1 to 2 minutes until slightly thickened.
Add heavy cream and peas. Taste and adjust seasoning.
Make dumpling dough: In a bowl, whisk flour, baking powder, salt, and garlic powder. Cut in cold butter until the mixture looks like coarse crumbs.
Stir in buttermilk and parsley until just combined. Do not overmix.
Drop the dumplings: Using a tablespoon or small scoop, drop rounded spoonfuls of dough onto the simmering surface. Leave a little space between each.
You should get 12 to 14 dumplings.
Steam gently: Cover the pot with a tight lid and reduce heat to low. Cook 12 to 15 minutes without lifting the lid. The dumplings should be puffed and cooked through.
Finish and serve: Remove the bay leaf.
Check a dumpling—no wet dough in the center. If needed, cover and cook 2 to 3 minutes more. Ladle into bowls and serve hot.