One hour before starting the cake, grate ½ teaspoon lime zest and mix it with ¾ cup sugar using the tip of your fingers so it starts to release oil. This will enhance the lime flavor. Reserve.

In a small bowl, stir 3 tablespoons lime juice with 1 cup unsweetened coconut. It will not moisten all the coconut, but that's fine. Mix to moisten and let soak for 1 hour. I tried it with more juice so more coconut was moistened, but there was too much lime flavor, and the coconut got a little bit lost. 

Butter or spray a 9-inch round springform cake pan. Reserve.

In a large bowl, sift 1 and ¼ cups flour, 2 teaspoons baking powder and ¼ teaspoon salt. Reserve.

Start beating ¾ cup unsalted butter in a large mixing bowl. Gradually add the lime sugar and beat for 2-3 minutes until creamy and light-colored. 

Add 3 eggs, one at a time, mixing well between each addition. 

Mix in the coconut with lime juice.

Stir in the flour mixture in 2 parts, beating on low speed until incorporated. Don't overmix it, or the cake will be less fluffy. 

Pour into the prepared pan and bake for 35 to 40 minutes, until a cake tester or toothpick inserted in the center comes out dry. 

Transfer to wire rack, let cool for 15 minutes and remove from the pan. Let cool completely before icing.

Mix 1 cup powdered sugar in a bowl with 2 tablespoons lime juice until smooth. 

Drizzle the glaze on top, letting it drip to the sides. of 

Top with shredded coconut and lime wedges. Let dry and serve. 

Store covered in plastic wrap or under a cake dome for 2 days at room temperature. Freeze leftovers for longer storage.