Rinse the Whole Chicken (4 pound) and place in a large dutch oven or heavy bottomed pot.
Add the diced Celery (3 stalk), diced Onion (1) and peeled and diced Carrot (3). Cover with Low-Sodium Chicken Broth (1 quart) and Water (2 cup), cover and bring to a boil.
Reduce heat to a simmer and cook for 30 minutes or until chicken is cooked through.
Remove the chicken from the pot and let cool for 10-15 minutes.
Meanwhile in a small skillet, heat the Olive Oil (2 teaspoon) over medium-high heat and add the Mushroom (8 ounce). Cook until browned and tender and set aside.
With clean hands, pick the meat off of the chicken, discarding the skin and bones.
Transfer the chicken back to the pot and stir in the quartered mushrooms. Place the pot back on the stove and hold it covered at a low simmer.
In a medium bowl, combine the Cornmeal (1/4 cup), Self-Rising Flour (1 cup), Kosher Salt (1/2 teaspoon), Granulated Sugar (1 1/2 teaspoon), and Fresh Chives (2 tablespoon).
Whisk to combine. Stir in the Milk (1/4 cup) and Half and Half (1/2 cup) to form a dough.
Drop the dumplings by tablespoonfuls onto the simmering liquid, cover (don't peek) and cook for 15 minutes.
Use a spoon to open up a space between the dumplings and pour in the Frozen Green Peas (1 cup). Gently stir the frozen peas into the broth and serve.