Heat oven to 350°F. Grease and line the bottom of an 8" round cake pan with a circle of parchment paper; set aside.
In the bowl of a stand mixer fitted with paddle attachment, beat butter, sugar, and vanilla on medium-high until pale and fluffy.
Add eggs one at a time, mixing until thoroughly combined. Mix in coconut oil.
In a large bowl, whisk together flour, shredded coconut, baking powder, and salt.
Starting and ending with the flour mixture, add flour mixture and coconut milk to butter mixture alternately. With mixer on low speed, mix until combined, being careful not to overmix. Scrape down bowl as necessary after each addition.
Spread batter into prepared pan, smoothing the surface with an offset spatula or the back of a spoon.
Bake for 35–40 minutes. Cake is done when a wooden pick inserted in the centre comes out clean with only a few fluffy crumbs attached.
Allow cake to cool for 10–15 minutes before removing from pan and transferring to a wire rack. Let cake cool completely.
Once cake is totally cool, let’s make buttercream! In the bowl of a stand mixer fitted with paddle attachment, cream butter and salt on medium speed until fluffy and smooth.
Sift in a third of confectioners’ sugar, then mix on low until fully incorporated. Scrape down bowl. Repeat two more times with rest of confectioners’ sugar.
Mix in skyr and vanilla, beating on high until light and fluffy, 4–5 minutes.
Spread frosting over cake with an offset spatula. Using the back of a spoon, make a large dip in the centre of the buttercream. Place chia smash into well, then sprinkle shredded coconut around buttercream rim.
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