Preheat the oven to 400 degrees F. Line 2 standard cupcake pans with 18 liners; set aside. In a bowl, whisk together flour, baking powder, and salt; set aside.
In a stand mixer or with an electric hand mixer, cream butter and sugar until smooth, 2-3 minutes. Add the eggs 1 at a time, blending well between each addition. And the vanilla and coconut extracts and mix until well combined, about 2 minutes.
Add half of the dry ingredients and blend, then add the coconut milk. Mix well. Blend in the remaining dry ingredients until just combined, then fold in the desiccated coconut.
Fill cupcake liners 3/4 of the way. Place tins in the oven and immediately drop the temperature to 350 degrees. Bake 19-20 minutes, checking at 15 for proper doming.
Remove from the oven and allow to cool in pan for 10 minutes, then transfer to cooling rack. When cool, use a cupcake corer or small knife to make a well in the center of each cupcake.
Place eggs and sugar in a medium saucepan and whisk to combine. Add lime juice, zest, and salt and whisk until smooth.
Place the saucepan over low heat. Stir constantly with a wooden spoon for 4-5 minutes until the mixture thickens. Remove from heat and add the butter, stirring until butter is melted and mixture is smooth.
Strain the curd through a fine mesh sieve into a mason jar or bowl; discard any solids. Cool curd to room temperature, then refrigerate, covered, until chilled.
Fill cored cupcakes with cold lime curd. Refrigerate any remaining curd in the jar for 2-3 weeks.
Lime Cream Cheese Buttercream:
Beat cream cheese and butter in a stand mixer, or in a large bowl with an electric hand mixer, on medium-high speed until combined and creamy, 4 to 5 minutes.
Add lime juice, zest, and 2-3 drops of green food coloring. Beat on low speed just until combined, stopping to scrape down sides of bowl as needed. Add powdered sugar and beat on low speed until incorporated, then increase speed to high and mix until smooth and well combined.
Refrigerate for at least 20 minutes before piping or spreading onto cooled, filled cupcakes. Sprinkle with shredded coconut and garnish with key lime slices.