In a large Dutch oven, bring chicken stock to boil.
Add chicken; cover and simmer over medium-low heat until juices run clear when chicken is pierced, about 30 minutes. With slotted spoon, transfer to plate; let cool. Remove meat from bones; cut into bite-size chunks.
Add carrots and potatoes to stock; cover and cook for 10 minutes.
Add pearl onions; simmer, covered, just until onions are tender, about 5 minutes.
With slotted spoon, transfer vegetables to plate. Pour stock into large measuring cup; if necessary, add more chicken stock to make 5 cups.
In same pan, melt butter over medium-high heat; cook celery, onion and mushrooms, stirring often, until softened, about 8 minutes.
Add flour, thyme, salt and pepper; cook, stirring, for 1 minute. Gradually whisk in reserved stock; bring to boil, stirring. Reduce heat to medium-low; simmer, stirring often, for about 5 minutes or until thick enough to coat back of spoon.
Return chicken and any accumulated juices to pan. Add carrot mixture, peas and cream, stirring to combine.
In bowl, whisk together flour, parsley, baking powder and salt.
Using pastry blender or 2 knives, cut in butter until in coarse crumbs.
Using fork, stir in enough milk to make sticky spoonable dough. Leaving space around each, drop by tablespoonfuls onto simmering stew; cover and cook, without lifting lid, for 15 minutes or until dumplings are no longer doughy underneath