How to Make It
Preheat oven to 325°F. Beat together granulated sugar and butter with an electric mixer on medium-high speed until very fluffy and pale, about 8 minutes. Reduce speed to medium-low and beat in eggs, 1 at a time, until combined, stopping to scrape down sides of the bowl as needed. (Mixture will look broken, but will come together when flour is added.) Reduce speed to low and gradually add flour and salt until just combined. Fold in 1 cup shredded coconut.
Generously grease a 12-cup Bundt pan with butter; coat inside of pan with ¼ cup shredded coconut, tapping out excess. Pour batter into pan and smooth the top. Bake until golden and a toothpick inserted in center comes out clean, 50 to 55 minutes. Cool in pan 15 minutes. Invert onto a wire rack and cool completely, about 1 hour.
For the glaze: Whisk together powdered sugar and 2 tablespoons of the milk in a small bowl until smooth. If needed, whisk in remaining 1 tablespoon milk, 1 teaspoon at a time, to create a pourable glaze consistency. Pour over cooled cake. Top with ¼ cup shredded coconut.