Preheat your oven to 350° F. Grease and line the bottom of two 8-inch square pans with parchment paper.
In a large bowl, sift in flour, baking powder, baking soda, and salt. Mix well and set aside.
In the bowl of an electric mixer fitted with the paddle attachment, mix the eggs and sugar until well combined. Gradually add in the oil and vanilla; mix until just blended.
With the mixer on low, slowly add half of the flour mixture and mix until just blended. Mix in the buttermilk, then slowly add remaining flour mixture, scraping down sides of the bowl with a spatula, as necessary, until just blended.
Divide batter evenly among the prepared pans. Bake for 15 to 20 minutes. Transfer pans to a wire rack and let cakes cool completely.
To prepare the chocolate icing, melt the butter and mix with milk. Whisk in cocoa powder until completely dissolved. Add in the confectioners' sugar, 1 cup at a time, and whisk slowly until thickened. Set aside.
To assemble, spread the jam over the top of one cake layer. Top it with another cake layer. Cut into 2-inch cake squares.
Put the coconut in a bowl and set aside.
Use forks to dip and turn a cake square into the chocolate icing to coat all sides. Allow excess icing to drip off, then place the square in the bowl with the coconut, turning it until it is completely covered. Place the square on a wire rack and allow to sit for at least 10 minutes to set. Repeat with all of the remaining squares.