The skillet is used in a few clever ways: Chicken and vegetables get a head start on the stove, finish in the oven, then come out briefly so a simple cream sauce can pick up all the roasted flavors in the pan.
Preheat oven to 425°.
Heat a large skillet over medium-high heat. Add oil; swirl to coat. Sprinkle chicken with 1/4 teaspoon salt and 1/4 teaspoon pepper. Add chicken to pan; cook 5 minutes or until golden brown. Turn and cook 2 minutes. Remove chicken from pan. Place carrots and potatoes, cut side down, in pan; sprinkle with thyme. Place pan in oven; bake at 425° for 10 minutes. Return chicken to pan; top with lemon slices. Bake at 425° for 12 minutes. Remove pan from oven. Place chicken and vegetables on a plate.
Combine 1/2 cup milk, flour, and rind in a bowl. Return pan to medium-high heat (do not wipe out pan). Add flour mixture, remaining 1 cup milk, and stock to pan, scraping pan to loosen browned bits; cook 3 minutes. Stir in remaining 1/2 teaspoon salt and 1/4 teaspoon pepper. Add chicken and vegetables to pan. Sprinkle with parsley.