Bring broth to a simmer in a medium saucepan. (Do not boil.) Keep warm over low heat.
Heat oil in a large saucepan over medium heat. Add leeks and mushrooms; sauté 5 minutes or until leeks are soft. Add rice; cook 1 minute, stirring constantly. Stir in wine; cook 1 minute or until liquid is nearly absorbed, stirring constantly. Add sage and warm broth, 1/2 cup at a time, stirring constantly until each portion of broth is absorbed (about 24 minutes total). Stir in cheese and pepper.