Jamie's Chicken and Dumplings

In a soup pot, melt the butter over medium heat. Whisk in the flour and stir 3-4 minutes until golden-brown. When golden brown, whisk in the Chardonnay and the chicken broth. Cook until the sauce has thickened, about 5 minutes, then add the celery, carrots, and onion. Cook the vegetables for about 15 minutes. Add the shredded chicken meat, heavy cream or milk, and peas. Season with salt and black pepper. Place the biscuit pieces on top of the chicken mixture. Cover and simmer until the biscuit pieces are cooked through, about 15 minutes. Serve in large soup bowls.