In a large skillet, melt the butter over medium heat. Add the onion, celery, and garlic. Cook until softened, about 4 minutes.
Stir in the flour, until all flour is absorbed. Then stir in the Worcestershire sauce, salt, pepper, and chicken bouillon.
Whisk in the chicken broth and cook until it begins to thicken just a little. Stir in the heavy whipping cream, then add the shredded chicken and peas. Pour the chicken mixture into a greased 9x13-inch pan.
Preheat the oven to 350°F.
Dumplings: In a medium-sized bowl, whisk to combine the flour, baking powder, baking soda, and salt. Stir in the milk and melted butter, until smooth. Dough should be spoonable. Add another tablespoon or two of milk if your dough is too thick.
Gently drop tablespoons of dough on top of the chicken mixture.
Bake uncovered, for 35 minutes, until the dumplings are cooked through.
Remove and let rest for 5 minutes, before serving.