Season Chicken from Chicken with Salt and Pepper. In a large pot or Dutch oven, brown Chicken in Olive Oil over medium-high heat; remove and set aside.
Add Onion, Carrots, and Celery from Vegetables to the pot and cook until softened, about 5-7 minutes. Add Mushrooms and cook for another 3-5 minutes.
Melt Butter from Sauce in the pot. Whisk in Flour and cook for 1-2 minutes to create a roux.
Gradually whisk in Chicken Stock from Sauce, ensuring no lumps form. Bring to a simmer. Stir in Sherry, Thyme, Rosemary, and Bay Leaf.
Return Chicken to the pot. Reduce heat and simmer for 45 minutes, or until chicken is cooked through.
While the stew simmers, prepare the Dumplings. In a bowl, whisk together Cornmeal, Flour, Baking Powder, Baking Soda, and Salt from Dumplings. Stir in Buttermilk until just combined.
Drop spoonfuls of Dumpling batter into the simmering stew. Cover and cook for 15-20 minutes, or until dumplings are cooked through.
Stir in Peas and Corn from Vegetables during the last 5 minutes of cooking.
