Preheat oven to 350°F (175°C). Grease and flour an 8.5 x 4.5 inch or 9 x 5 inch loaf pan, or line with parchment paper, leaving an overhang on the long sides.

In a medium bowl, whisk together the sifted all-purpose flour, baking powder, and salt. Set aside.

In a large mixing bowl, using an electric mixer, cream together the softened unsalted butter and granulated sugar on medium speed until light and fluffy, about 2-3 minutes.

Add the eggs one at a time, beating well after each addition until fully incorporated. Scrape down the sides of the bowl as needed. Beat in the vanilla extract.

With the mixer on low speed, gradually add about one-third of the dry ingredients to the butter mixture, mixing until just combined.

Pour in half of the coconut milk and mix until just incorporated.

Repeat with another third of the dry ingredients, then the remaining coconut milk, and finally the last third of the dry ingredients. Mix until just combined, being careful not to overmix.

Gently fold in the shredded unsweetened coconut with a rubber spatula until evenly distributed.

Pour the batter into the prepared loaf pan and spread evenly.

Bake for 50-60 minutes, or until a wooden skewer inserted into the center of the cake comes out clean. If the top browns too quickly, tent loosely with aluminum foil.

Remove the loaf cake from the oven and let it cool in the pan on a wire rack for 15-20 minutes.

Carefully invert the cake onto the wire rack to cool completely before glazing.

While the cake cools, prepare the glaze. In a medium bowl, whisk together the sifted powdered sugar and fresh lime juice until smooth. If the glaze is too thick, add an optional tablespoon of coconut milk, a little at a time, until you reach a pourable but still thick consistency.

Once the loaf cake is completely cool, drizzle the lime glaze evenly over the top, letting it drip down the sides.

Garnish with optional lime zest and toasted shredded coconut if desired.

Allow the glaze to set for about 15-20 minutes before slicing and serving.