Combine water and chicken in a large Dutch oven; bring to a boil. Reduce heat to medium, and cook, uncovered, 1 hour. Remove from heat. Remove chicken from cooking liquid (broth); place chicken in a bowl, and chill for 15 minutes. Remove skin from chicken, and remove meat from bones, discarding skin and bones. Chop chicken into bite-size pieces; cover and chill. Strain broth through a sieve into a large bowl; discard solids. Skim fat from surface; discard. Reserve 6 cups broth.
Heat the oil in the pan over medium-high heat. Add the leek, basil, thyme, and oregano; sauté 5 minutes or until leek is browned. Add reserved broth, scraping pan to loosen browned bits. Stir in the turnips and rice; bring to a boil. Reduce heat, and simmer for 30 minutes or until turnips are tender. Partially mash turnips with a potato masher. Add chicken, milk, and salt, and cook 5 minutes or until thoroughly heated. Remove from heat, and add cheese, stirring until melted.