In a large pot or dutch oven, add in split chicken breasts, water, salt and bay leaves. Bring to a boil and cook over medium heat for 45 minutes.
Remove chicken from pot and let cool before shredding. Remove bay leaves from the stock.
Add chopped vegetables to the stock and cook for 10 minutes.
In a separate saucepan, make a roux by melting butter and whisking in flour. Cook for 30 seconds, then gradually add stock to thin it out.
Add the roux mixture back to the pot with the vegetables. Whisk until no lumps remain, then add cream and peas.
Bring to a light boil and add the dumplings one by one. Cover and cook for 10 minutes until dumplings are tender.
Remove from heat and stir in the shredded chicken to heat through.
For the dumplings: In a medium bowl, combine flour, baking powder and salt. Add melted butter and milk, stirring just until combined. Turn out onto a floured surface and knead briefly. Roll out to ⅛" thick and cut into 1" strips and 3-4" pieces.
