Bring 1 3/4 cups water and 1 tablespoon butter to a boil in a saucepan. Stir in rice and seasoning packet; return to a boil. Cover, reduce heat to low, and simmer until rice is tender and water is absorbed, 20 to 25 minutes. Fluff rice with a fork.
Heat 3 tablespoons butter in a separate saucepan over medium heat. Add figs and currants; toss to coat. Cook and stir until heated through, about 2 minutes. Add mango and water; cook and stir until mango is softened and dried fruit has absorbed water, about 5 minutes.
Stir cashews and half-and-half into fruit mixture; cook until sauce is thin and slightly reduced, about 5 minutes. Add chicken and blue cheese; cook until chicken is warmed and blue cheese is melted, about 5 minutes. Serve over rice pilaf.