In a 6-quart dutch oven, cook chicken over medium-high heat until brown on both sides. Once chicken pieces are browned, remove and set aside.
Add carrot and onion and cook until just tender, about 3 minutes.
Add garlic and stir for another minute.
Reduce heat to medium-low and add butter and flour, stirring constantly for 3 minutes to avoid lumps.
Add chicken and any accumulated juices back to dutch oven and stir to to coat in roux/vegetable mix. Add chicken broth, cream, thyme, and bay leaves and bring to a simmer. Once soup is at a simmer, add frozen peas and cover.
In a separate bowl, combine flour, baking powder, salt, pepper, and cream. Stir until mixture comes together into single mass of dough.
Using a large spoon or ice cream scoop, form dough into small round balls about 1 inch in diameter (this dough mixture should yield 14-16 dumplings).
Place dough balls into simmering soup (making sure they don’t touch), and cover. Let soup simmer for 15 minutes or until dumplings are cooked (they should pass the toothpick test).