Preheat the oven to 300 degrees F. Line a baking sheet with parchment paper and brush with the butter.
Place the egg whites in a clean, dry mixing bowl. Beat the egg whites until firm peaks, adding the sugar, salt and cream of tartar to the mixing bowl halfway through beating. Gently fold the coconut and 3/4 cup pistachios into the egg whites. Dollop the mixture onto the baking sheet and sprinkle with the remaining pistachios.
Bake until firm and lightly golden, 20 to 30 minutes. Place on a cooling rack.