Place a rack in center of oven and preheat to 325 degrees. While oven preheats, place coconut in a small baking pan and toast until brown around the edges, about 10 minutes. Remove and cool. Grease and flour a 9-inch loaf pan and set aside.
Next, place butter and sugar in a large bowl and cream with electric mixer on medium speed until soft, 1 minute. Set aside.
Separate the eggs, placing whites in a large bowl and setting aside. Place yolks in a small bowl. Drop yolks, one at a time, into the butter mixture and beat on low until combined.
Stir together flour, coconut flour, and salt in a medium-size bowl, and add this to the butter mixture along with vanilla and milk. Beat on medium-low until combined and smooth.
Using clean beaters, beat egg whites on high speed until stiff peaks form, about 3 minutes. Using a rubber spatula, fold whites into batter until completely incorporated. Fold in toasted coconut. Pour batter into pan and place in oven.
Bake until loaf is deeply golden brown, about 58 to 62 minutes, then let it rest in pan on a rack for 20 minutes. Run a knife around the outside edges of the pan, loosening cake, then invert it onto a rack to completely cool, about 1 hour. Slice and serve.