Preheat oven to 350°. Combine the first five ingredients; beat on low speed until moistened, about 30 seconds. Beat on medium for 2 minutes; stir in coconut and toasted pistachios.
Pour into two greased 8-in. round baking pans or a greased 13x9-in. baking pan. Bake until a toothpick inserted in the center comes out clean, 40-45 minutes. Cool on a wire rack.
For frosting, beat milk and pudding mix on low speed for 2 minutes. Fold in whipped topping. Spread frosting over top of cake, and, if using round pans, between layers. Top with toasted coconut and pistachios. Refrigerate until serving.
