Make the cupcakes:

1. Preheat oven to 350 degrees Fahrenheit and line 2 cupcake tins with 18 cupcake liners (if you only have one cupcake tin, you may bake them in two batches).
2. Melt the coconut oil for 45 seconds in the microwave, set aside, and allow to cool.
3. In a medium-sized mixing bowl, whisk together 2 1/4 cups gluten free flour, 2 teaspoons baking powder, 1/2 teaspoon baking soda, and 3/4 teaspoon salt.
4. Open the can of coconut milk, pour into a bowl, and whisk until uniform.
5. In a medium sized mixing bowl with a handheld mixer or in the bowl of a stand mixer, mix 1 1/2 cups sugar, 1/2 cup melted coconut oil, 1 cup coconut milk, and 2 teaspoons of vanilla on medium speed for 30 seconds. Add 3 eggs, one at a time, mixing after each one is added.
6. With the mixer on low, add the flour mixture one half at a time. Once fully incorporated, mix on high speed for 1 minute. Mix in 1 1/4 cups coconut by hand with a rubber spatula or on low until incorporated.
7. Fill cupcake liners 3/4 of the way full and bake for 12-15 minutes on the middle rack of the oven checking on them after 12 minutes. They are done once a toothpick or cake tester comes out clean or with a couple crumbs.
8. Frost cupcakes after they have cooled completely.

Make the white chocolate buttercream:

1. In a large mixing bowl with an electric mixer or in the bowl of a stand mixer with a whisk attachment, place 1/2 cup (1 stick) of vegan/dairy free butter and mix on high speed until the butter is softened and has a creamier consistency (about 1 minute).
2. With the mixer on low, add in 2 1/2 cups powdered sugar 1/2 cup at a time, mixing on high for 15 seconds after each addition scraping the sides of the bowl with a rubber spatula as necessary.
3. Add 1 teaspoon of vanilla and 1 tablespoon coconut milk and mix on high for 1 minute more. You may stop at this point for vanilla buttercream or continue on to make white chocolate buttercream.
4. Melt 6 ounces (approximately 3/4 cup) dairy free white chocolate. Place white chocolate into a small microwave safe bowl and microwave for 1 minute on 50% power. Stir. Microwave 30 seconds. Stir. Microwave 15 seconds more until completely melted. Do not overheat.
5. With the mixer running on high speed, pour the white chocolate into the buttercream and mix on high speed 30 seconds.
6. Frost cupcakes after they have cooled completely.