Preheat oven to 325° F. Grease doughnut pan and line a baking sheet with parchment paper.
Spread the shredded coconut into a thin, even layer on the prepared baking sheet. Place in oven for 3-4 minutes. Remove and toss the coconut with a spatula. Place back in oven and toast for an additional 3-4 minutes, or until coconut has browned slightly. Remove and allow to cool completely before transferring the coconut to a small bowl.
In a large bowl, whisk together the egg, oil and buttermilk. Stir in contents the of the doughnut mix. Mix until well combined.
Pipe or spoon batter into doughnut well, filling each half full. Bake 10-15 minutes. Allow to cool in the pan for about 10 minutes before carefully removing them to a wire rack to cool completely.
While the doughnuts are cooling, combine the glaze mix with 2 tablespoons of melted butter. Slowly add milk, one tablespoon at a time, until the glaze is at desired consistency. Whisk until very smooth.
When the doughnuts and toasted coconut are completely cool, dip the tops of the doughnuts into glaze and then dip them into the toasted coconut, allowing the coconut to adhere to the glaze. Set aside and let the glaze set completely.
When the glaze has set, place 3 candy coated chocolate eggs into the center of each doughnut and serve.