For the stew: Bring broth to simmer in Dutch oven over high heat. Add chicken and return to simmer. Cover, reduce heat to medium-low, and simmer until chicken is just cooked through, about 10 minutes. Transfer chicken to plate and tent loosely with aluminum foil. Transfer broth to large bowl.
Return empty Dutch oven to medium-high heat and melt butter. Add carrots, onion, and salt and cook until softened, about 7 minutes. Grate in garlic and stir until fragrant, about 30 seconds. Stir in flour and cook, stirring frequently, for 1 minute. Stir in sherry, scraping up browned bits. Stir in reserved broth, cream, thyme, bay leaves, and pepper and bring to boil. Cover, reduce heat to low, and simmer until stew thickens, about 20 minutes.
For the dumplings: Stir flour, baking powder, and salt in large bowl. Stir in cream until incorporated (dough will be very thick and shaggy).
Discard bay leaves and return stew to rapid simmer. Shred reserved chicken and add to stew along with any accumulated juices, peas, and 3 tablespoons parsley. Using 2 large soup spoons or a small ice cream scoop, drop golf ball-sized dumplings onto stew about 1/4 inch apart (you should have 16-18 dumplings). Reduce heat to low, cover, and cook until dumplings have doubled in size, 15 to 18 minutes. Garnish with remaining parsley and serve.