Spring Chicken with Carrot Broth and Baby Carrots

Name: Spring Chicken with Carrot Broth and Baby Carrots
Ingredients: 1¼ cups baby carrots, peeled; 1 teaspoon extra-virgin olive oil; 1 medium carrot--peeled, cut and sliced on the bias into 1-inch lengths; ½ small white onion, thinly sliced; 1 garlic clove, thinly sliced; One 1 inch-long piece of ginger, peeled and thinly sliced; 1/8 teaspoon ground turmeric; 3 sprigs thyme; Salt; 5 whole black peppercorns; 1½ cups vegetable stock; 1½ cups carrot juice, preferably fresh; 1½ teaspoons fresh lemon juice, divided; 4 skin-on, bone-in chicken breasts (about 3 to 4 pounds); 1 tablespoon vegetable oil; 1 teaspoon unsalted butter; 10 ounces fresh fettuccine noodles