Heat the oven to 350 degrees. Spray with baking spray a 10- or 12-cup Bundt pan, making sure to get into all the grooves of the pan. In large bowl, whisk together the flour, baking powder, and salt; set aside.
In the bowl of your stand mixer, cream butter and sugar until pale and fluffy using the paddle attachment (you could also beat it with a hand mixer), 4-5 minutes. Beat in the eggs one by one, waiting until each has been incorporated to add the next. Be sure to scrape the mixing bowl after each addition of the eggs. Add the vanilla and mix to combine. Add in the lime zest and mix well.
Add half of the flour mixture to the mixer beat on low speed until incorporated. Scrape down the sides of the bowl to incorporate.
Add in the coconut milk (or buttermilk) and shredded coconut. Beat until incorporated followed by the remaining flour mixture; scrape the sides of the bowl to incorporate.
Tap the pan heavily on the counter a few times to help even out the batter and remove air pockets. Bake for 45-50 minutes, or until a toothpick inserted into the center of the cake comes out clean and the top springs back when lightly pressed.
Let the cake cool in the pan for 15 to 20 minutes.
When the cake is done, allow it to cool in the pan for 10 minutes. Carefully remove cake by flipping from pan onto your serving plate.