Adjust the oven rack to middle position and heat to 350°F. Grease and flour an 8½ by 4½-inch loaf pan. Whisk flour, baking powder, and salt in a bowl.

Process sugar, cream of coconut, eggs, vanilla, and coconut extract in a food processor for 10 seconds. With the machine running, pour the melted butter through the feed tube for 30 seconds. Pour mixture into a bowl.

Sift one-third of the flour mixture over the egg mixture and whisk in. Repeat twice more with remaining flour mixture, whisking gently until most lumps are removed (do not overmix).

Pour batter into the prepared pan and smooth top. Tap the pan gently on the counter to settle the batter. Bake until a skewer comes out with a few crumbs attached, about 50 to 60 minutes, rotating halfway through.

Let cake cool in the pan for 10 minutes, then flip onto a wire rack. Let cool completely, about 2 hours before serving.