How to Make It
Pat chicken dry with paper towels. Sprinkle chicken with paprika and 3/4 teaspoon each of the salt and pepper. Melt butter in a large enamel-coated cast-iron skillet with lid over medium-high. Place half of chicken, skin side down, in skillet; cook until skin is golden brown, about 6 minutes. Remove chicken from skillet; repeat process with remaining chicken.
Add carrots to pan, and cook, stirring occasionally, until browned, about 7 minutes. Add flour to skillet; cook, stirring often, 1 minute. Add broth, thyme, and remaining 1/4 teaspoon salt and pepper; bring to a boil. Place chicken, skin side up, on carrots. Partially cover with lid; reduce heat to medium-low, and cook until chicken is done, about 20 minutes. Remove thyme sprigs. Stir in lemons, and, if desired, serve over mashed potatoes.