Chicken and Dumplings

Name: Chicken and Dumplings
Prep time: 15 min
Cook time: 3 h 5 min
Total time: 3 h 20 min
Cuisine: European
Ingredients: 1 (3-pound) whole chicken; Salt and freshly ground black pepper; 4 ounces unsalted butter, softened; 1 lemon, halved and juiced; halves reserved; 1/4-cup fresh chopped herbs, such as thyme, parsley and rosemary; 1 onion, halved; 4 garlic cloves, smashed; Fresh whole herbs, such as rosemary, thyme and parsley sprigs; 2 tablespoons olive oil; 2 carrots, cut in large chunks; 2 celery stalks, cut in large chunks; 1 onion, halved; 1 garlic bulb, halved; Reserved chicken bones; 2 quarts cold water; 4 sprigs fresh parsley; 4 sprigs fresh thyme; 2 bay leaves; 2 cups flour; 1 tablespoon baking powder; 1 teaspoon salt; 2 eggs; 3/4 to 1 cup buttermilk; 2 tablespoons butter; 1 tablespoon oil; 1/2 cup diced carrot; 1/2 cup diced celery; 3 cloves garlic, minced; 2 bay leaves; 1/4 cup flour