Add the chicken broth and half and half, alternating between the two, whisking until smooth. Add the salt, black pepper, and nutmeg. Return the vegetables to the skillet and simmer until all the vegetables are just tender.
Meanwhile, cook the stovetop stuffing mix according to package directions and cover to keep warm.
Add the chicken and peas to the skillet and cook for 2 minutes. Pour the chicken-vegetable mixture into the prepared baking dish. Spoon the cooked stuffing on top.
Bake in the oven for 25 minutes or until lightly browned. If desired, top with some chopped fresh herbs.
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