In a large Dutch oven, heat olive oil over medium-high heat. Once hot, add the chicken pieces, seasoning with Kosher salt and black pepper. Cook until they are no longer pink, about 6 to 8 minutes, then remove them to a plate and set aside.
Melt butter in the same pot, adding the chopped onion and sliced carrots. Cook for 3 to 5 minutes, stirring occasionally until the vegetables become tender. Add the minced garlic and stir for another 30 to 60 seconds until fragrant.
Reduce the heat to medium-low, then sprinkle all-purpose flour over the vegetables. Stir constantly for about 2 minutes, allowing the flour to cook slightly.
Return the cooked chicken to the pot along with any juices from the plate. Stir to combine.
Pour in the chicken broth, heavy cream, thyme, bay leaf, and additional salt and pepper to taste. Increase the heat to bring the mixture to a simmer, then add the frozen peas and cover the pot. Let it cook for about 15 minutes.
While the soup is simmering, prepare the dumplings. In a large mixing bowl, whisk together flour, baking powder, salt, and black pepper. In a separate measuring cup, whisk together milk and melted butter until well combined.
Add the wet mixture to the dry ingredients, stirring just until moistened. The batter should be slightly lumpy but not dry.
Using a large spoon or cookie scoop, portion the dumpling dough into 1-inch round balls. Carefully drop the dough balls into the simmering soup, making sure they don’t touch each other.
Once all the dumplings are added, cover the pot and allow the soup to simmer for an additional 15 minutes, or until the dumplings are cooked through and fluffy. The steam will help them rise.
Remove the lid, stir in the chopped parsley, and serve the hot soup and dumplings in shallow bowls. Garnish with additional parsley if desired.