Heat oven to 375°F with rack positioned just under center.
FOR THE STEW:
Cut chicken into 2 to 3-inch pieces. Combine dredging ingredients in a resealable bag. Place chicken in the bag and shake bag to lightly coat chicken with seasoned flour. In a 6 quart ovenproof pot, heat 2 to 3 tablespoons of oil over med heat. Working in batches, carefully place the floured chicken pieces, shaking off excess, to the pot. Brown each side about 2 minutes on each side and transfer to a paper towel-lined platter. *Add oil as needed between batches so that it just covers the bottom of the pot. Once all the chicken is browned, there should be a little oil left in the pot.
Add the carrots, mushrooms, onion, celery, garlic, thyme, bay leaf, salt and pepper to the pot with the oil (add more if needed). Cook over medium heat for 8-10 minutes, or until vegetables soften and begin to caramelize.
Add the sherry and stir to scrape up any browned bits from the bottom; simmer briefly until sherry is nearly evaporated. Sprinkle 3 tablespoons flour over vegetables and stir so the flour is absorbed. Gradually add broth and stir.
Return chicken to pot, stir in cream and parsley, then bring to a low simmer. While the stew is simmering, make the dumplings.
FOR THE DUMPLINGS:
In a medium mixing bowl, stir the flour, Parmesan, baking powder, sugar, salt and pepper together until well mixed.
In a small saucepan, heat milk and butter over medium-high heat until butter melts. Pour the milk and butter mixture into the dry mixture and stir with a fork or spoon until just combined and flour is moistened - careful not to over-mix or over-handle the dough. The hot milk sets the starch so the dumplings don't fall apart.
Using a spoon, scoop segments of the dough (about the size of a golf ball) and place gently on top of the simmering stew. The dumplings should rest on top.
Cover with the lid and slide the pot into the oven to bake for 20 minutes. It is important to not lift the lid during this time so the steam inside cooks the dumplings.
Fresh Herb Dumplings: Add 1-2 tablespoons of fresh herbs like savory, thyme, basil, or parsley to the dumpling flour mixture just before stirring in the milk.
White meat instead of dark meat: Chicken thighs are very forgiving, so if using boneless and skinless chicken breasts, reduce browning time to 1 minute on each side and return the chicken to the pot to simmer 1-2 minutes before adding the dumplings.
Make Chicken and Dumplings with Rotisserie Chicken:
Step 1 ~ Remove rotisserie chicken from the bones and tear or cut chicken into larger bite-size chunks. Set aside.
Step 2 ~ Add 2 tablespoons of oil to a 6 quart ovenproof pot and follow the rest of the recipe as written.