Old-Fashioned Chicken and Dumplings

Name: Old-Fashioned Chicken and Dumplings
Prep time: 10 min
Cook time: 30 min
Total time: 40 min
Cuisine: American, Southern
Ingredients: 2 lbs boneless, skinless chicken breasts and/or thighs, trimmed and cut into 1 1/2-inch pieces; 1/2 cup all-purpose flour; 2 tablespoons olive oil, divided; 2 tablespoons butter; 2 large carrots, peeled and diced; 2 stalks celery, diced; 1 large onion, diced; 2 bay leaves; 1/2 teaspoon dried thyme; 2 cloves garlic, minced; 5-6 cups chicken broth; 1/2 cup heavy cream; 1 1/2 cups frozen peas, thawed; 1 1/2 cups all-purpose flour; 2 teaspoons baking powder; 1/2 teaspoon salt; 3/4 cup buttermilk; 2 eggs; Kosher salt and freshly ground black pepper, to taste