In a 3- to 4-quart pan over high heat, bring 2 quarts water to a boil. Add green beans and cook just until they turn bright green and are tender-crisp, 30 seconds. Drain and immediately rinse under cold running water until cool to touch. Cut beans diagonally into 1-inch lengths.
Pour oil into a 12-inch nonstick frying pan or 14-inch wok over high heat. When hot, add garlic, half the green onions, and half the chilies. Stir until fragrant, 1 minute. Add ground turkey and stir frequently until very little pink remains and turkey is crumbly, about 5 minutes.
Meanwhile, in a 2-cup glass measure, mix chicken broth, brown sugar, fish sauce, soy sauce, and pepper. Pour over turkey mixture and stir until liquid is partly evaporated and turkey is no longer pink in center of thickest pieces (cut to test), about 4 minutes. Stir in green beans and 3/4 cup chopped basil.
Pour into a serving bowl and sprinkle with the remaining basil, green onions, and sliced chilies. Top with the cashews. Serve alongside hot cooked jasmine rice.