Saute chopped leeks in extra-virgin olive oil until softened; add quick cooking barley. Cook and stir for 1 minute. Add hot chicken stock, 1/2 cup at a time, stirring in each addition until the liquid is absorbed. When liquid is absorbed and mixture is creamy (about 25 minutes), remove saucepan from heat; stir in Parmesan cheese, shredded carrots, and tarragon. Makes 4 to 6 servings.