Note: Make the dumplings just before adding them to the stew.
For the stew: Melt butter in medium saucepan over medium-high heat. Add carrots and onion and cook until lightly browned, 5 to 8 minutes. Add garlic, thyme, 1/2 teaspoon salt, and 1/2 teaspoon pepper and cook until fragrant, about 30 seconds. Add flour and cook, stirring, for 1 minute. Stir in sherry, scraping up any browned bits, and cook until nearly dry, about 1 minute. Slowly stir in broth and bring to boil. Add chicken, reduce heat to medium-low, cover, and simmer until chicken is cooked through and tender, about 15 minutes.
For the dumplings: Combine flour, baking powder, and salt in bowl. Stir in broth and melted butter until just incorporated.
Season stew with salt and pepper to taste. Increase heat to medium. Using 2 spoons, drop eight 1-inch dumplings into stew about 1 inch apart. Cover and simmer for 5 minutes. Sprinkle peas around dumplings, cover, and cook 5 minutes longer. Remove from heat and let cool slightly, uncovered, about 10 minutes. Serve.