Grease and flour a 9x5-inch loaf pan.
In a medium bowl, combine cake flour, baking powder, and salt. Whisk until blended.
In a small saucepan over medium heat, melt the butter.
Continue cooking the butter until it turns golden brown and forms brown flecks, about 6-8 minutes. Stir frequently to prevent burning on the bottom.
Remove the butter from heat, set aside, and allow to cool for about 10 minutes.
In a large mixing bowl, combine sugar, dark rum, eggs, and extracts, beating until well-blended.
With the mixer running on low, add the melted butter in a slow and steady stream.
Add the flour mixture to the mixing bowl, and beat until just combined.
Fold in the shredded coconut.
Pour batter into prepared pan and level with a rubber spatula.
Bake at 350 degrees for 15 minutes, then reduce oven temperature to 325 degrees, and continue baking for about 40-45 minutes, or until the top is golden brown and a toothpick inserted near the center comes out clean.
Cool in pan for 10 minutes, then turn cake out onto a wire rack to cool completely.