Preheat the oven to 350 degrees F. Butter 3 (8-inch) round cake pans and line with parchment paper. In a medium size bowl, combine the flour, baking powder, baking soda, and salt.
In the bowl of a stand mixer (or use a hand-held mixer) beat together the butter and sugar until light and fluffy. With the mixer on low, beat in the eggs, one at a time, until incorporated. Add the greek yoghurt and vanilla and beat until combined. Slowly add the dry ingredients to the wet ingredients with the mixer on low, alternating with the milk and ending with flour until just combined.
Remove 1/3 of the batter (about 3 cups) and spread in 1 of the prepared cake pans. Set aside.
To the remaining batter, beat in the cocoa powder and coffee. Divide the chocolate batter evenly between 2 cake pans. Transfer all 3 cakes to the oven and bake 25-30 minutes, until the tops are just set and no longer wiggly in the center. Remove and let cool five minutes, then run a knife around the edges of the pan and turn the cakes out onto a cooling rack. Cover and let the cakes cool completely before assembling.
To make the frosting. Beat the butter and powdered sugar in the bowl of a stand mixer until the butter is light and fluffy, about 4 minutes. Add the vanilla and beat until combined. Remove 1 cup of the vanilla frosting and set aside.To the remaining frosting, add the cocoa powder and cream and whip the frosting for 2-4 minutes more or until light and fluffy.
Place a chocolate layer on a plate or cake stand and spread the top with chocolate frosting. Place the vanilla cake on top and spread with vanilla frosting. Add the final chocolate layer and frost the top and sides of the cake with chocolate frosting. If desired, you can alternate between chocolate and vanilla frosting to create a marbled, swirled look. Slice and serve. Enjoy!