Preheat oven to 325°F (165°C). Grease a 9x5-inch loaf pan, line it with a strip of parchment paper with overhang, and lightly grease the parchment.

Beat the softened butter and granulated sugar together with a mixer on medium speed until very light and fluffy, about 3–4 minutes.

Add the eggs one at a time, beating well and scraping down the bowl after each addition, then mix in the vanilla and coconut extract until smooth.

In a separate bowl, whisk together the all-purpose flour, baking powder, and fine sea salt until well combined.

In another bowl, whisk the canned coconut milk and sour cream or Greek yogurt until completely smooth.

With the mixer on low speed, add the dry ingredients to the butter mixture in three additions, alternating with the coconut milk mixture, beginning and ending with the dry ingredients. Mix just until combined.

Gently fold in the well-drained crushed pineapple, shredded sweetened coconut, and rum if using, until evenly distributed through the batter.

Scrape the batter into the prepared loaf pan and smooth the top, then tap the pan lightly on the counter to release any large air bubbles.

Bake for 60–70 minutes, or until the top is deep golden and a toothpick inserted into the center comes out with just a few moist crumbs. Tent loosely with foil during the last 15–20 minutes if the top is browning too quickly.

Allow the cake to cool in the pan for 15 minutes, then use the parchment overhang to lift it out onto a wire rack. Cool completely before glazing.

To make the glaze, whisk the powdered sugar with 3 tablespoons canned coconut milk until thick but pourable, adding up to 1 more tablespoon coconut milk if needed to reach a smooth, drizzleable consistency.

Drizzle the coconut glaze generously over the cooled cake, letting it drip down the sides, then sprinkle with toasted shredded coconut, pineapple pieces, and lime zest if using.

Slice with a sharp serrated knife and serve. Store leftover cake covered at room temperature for up to 3 days, or refrigerate for up to 5 days and bring slices to room temperature before serving.