Zest and juice the limes and set the juice and zest aside. (I needed 6 small limes.)
Preheat the oven to 350F and line an 8x4 loaf pan with parchment paper.
To a measuring cup, add the coconut milk, lime juice and vanilla extract; stir to combine and set aside.
To a small bowl, add the flour, baking powder, and baking soda; whisk to combine and set the bowl aside.
To a medium bowl, add the sugar and lime zest. Rub the zest into the sugar with your fingers until all of the sugar is coated in the zest.
Add the butter and oil to the bowl with the sugar. Using a hand held mixer, blend the sugar, oil and butter together on medium speed until well combined - about 2 minutes.
Add a 3rd of the dry ingredients to the sugar mixture and blend on medium speed for about 15 seconds, add a 3rd of the wet ingredients and blend at medium speed for about 15 seconds. Repeat this 2 more times with the rest of the dry and wet ingredients.
Add the shredded coconut to the batter and fold it in.
Pour the batter into the prepared pan and bake for 55 to 60 minutes. The loaf should be just starting to brown and a toothpick inserted should come out clean.
Let the loaf rest in the pan for 10 minutes and then transfer it to a cooling rack.