Make a presentation statement of this chicken and vegetable dinner recipe by wrapping a 16x2-1/2-inch strip of parchment paper around each individual dish and tying with 100 percent cotton string before baking.
Preheat oven to 400 degree F. Arrange chicken in a 13x9x2-inch baking pan. Season lightly with salt and pepper. Bake for 20 minutes or until chicken is no longer pink and juices run clear; set aside.
Meanwhile, cook the fresh peas, if using, in a small amount of boiling lightly salted water for 2 minutes; drain. For the sauce, in a medium saucepan combine 2 tablespoons of the melted butter and chopped onion. Cook and stir over medium heat for 5 minutes or until onion is tender. Stir in peas, the 1/3 cup flour, and tarragon. Add chicken broth all at once. Cook and stir over medium heat until thickened and bubbly. Cover and keep warm while preparing cobbler topping.
For cobbler topping, in a medium mixing bowl stir together the 2 cups flour, shredded carrot, sugar, baking powder, and the 1/2 teaspoon salt. Stir in milk and the remaining 2 tablespoons melted butter until combined. Place a baked chicken thigh in each of six individual ungreased 10-ounce custard cups, ramekins, or baking dishes. Pour warm sauce over the chicken. Spoon topping over sauce. Place dishes in a 15x10x1-inch baking pan. Bake for 25 minutes or until topping is golden brown and a wooden toothpick inserted in the center of topping comes out clean. Makes 6 srvings.