Chicken and Dumplings

I have been looking for a good chicken and dumpling recipe for years, and this one hits the spot (though, I have to admit, I don't consider this recipe easy to quick like the website says). Nate was very excited about it, and my kids loved it. I've put some changes I'll do next time below in italics.

The Ultimate Chicken and Dumplings
Tyler Florence
Food Network website

Chicken and Stock:
1 (3 to 31/2 pound) whole organic chicken
2 bay leaves
6 sprigs thyme
4 to 5 black peppercorns
1 head garlic, split through the equator
2 tablespoons salt

Buttermilk-Chive Dumplings: I think I'll halve this part next time; I had a lot of leftover batter.
2 cups all-purpose flour
1 tablespoon baking powder
1 teaspoon salt
2 eggs
1/4 cup chopped chives
3/4 to 1 cup buttermilk

Sauce:
2 tablespoons butter
2 tablespoons oil
2 carrots, diced
2 stalks celery, diced
2 cloves garlic, minced
2 bay leaves
1/4 cup all-purpose flour
6 cups chicken stock
1 cup frozen peas
1 cup frozen pearl onions I think I'll chop a regular onion and saute it with the carrots, celery and garlic. Nate and I didn't like the pearl onions, though I suspect it's more traditional this way
1/4 cup heavy cream Forgot to put this in but didn't miss it.
Freshly ground black pepper, for garnish
Chopped chives, for garnish

For the stock:
Place the chicken and all stock ingredients in a large Dutch oven and cover with water. Set over medium-high heat and bring to a boil. Reduce heat to a simmer and cook for 1 hour until the chicken is tender. Skim the surface of fat and scum as it cooks. I cooked my chicken in the crock pot using the same ingredients all day until I was ready to make dinner.

When done remove the chicken to a cutting board. Strain the stock and shred the meat into big pieces - the stock will be used for the sauce and the chicken will be folded into it.

For the dumplings:
Sift the dry ingredients together in a large bowl. In a small bowl, using a whisk, lightly beat the eggs, chives and buttermilk together; pour the liquid ingredients into the dry ingredients and gently fold. Mix just until the dough comes together; the batter should be thick and cake-like.

To prepare sauce:
In a Dutch oven, over medium heat, add the butter and oil. Add the carrot, celery, garlic, and bay leaves and saute until the vegetables are soft, about 5 minutes. Stir in the flour to make a roux. Continue to stir and cook for 2 minutes to coat the flour and remove the starchy taste. Slowly pour in the chicken stock, 1 cup at a time, stirring well after each addition. Add frozen peas and pearl onions.

Let sauce simmer until it is thick enough to coat the back of a spoon, about 15 minutes. Stir in heavy cream.

Fold the reserved shredded chicken into the sauce and bring up to a simmer. Using 2 spoons, carefully drop heaping tablespoonfuls of the dumpling batter into the hot mixture. The dumplings should cover the top of the sauce, but should not be touching or crowded. Let the dumplings poach for 10 to 15 minutes until they are firm and puffy. Remove and discard the bay leaves. Season with freshly cracked black pepper and garnish with chopped chives before serving.