Preheat the oven to 350°F. Grease a tube pan or two 9-inch cake rounds and line with parchment. Have a baking sheet ready.
In a large bowl, whisk together the flour, sugar, cocoa, baking soda, baking powder and salt. In a medium bowl, combine the yogurt, milk, olive oil, eggs and vanilla. Slowly add the wet ingredients to the dry using a wooden spoon or rubber spatula. Then add the coffee and whisk lightly or stir just to combine, scraping the bottom of the bowl with a rubber spatula.
Pour the batter into the prepared pan, place the pan on the baking sheet to catch any drips, and place in the oven, and bake for 35-40 minutes, until a cake tester comes out clean. Remove from oven and cool in the pan for 30 minutes, then carefully turn the cake out onto a cooling rack and cool completely before frosting.
Make Frosting
Melt the chocolate over a double boiler or a metal bowl set over a pot of simmering water. Set aside to cool slightly.
In a large bowl, whip the butter with a mixer until it is smooth and fluffy. Add the melted chocolate and the powdered sugar and whip to combine, then add the milk (more if needed) to make a smooth, fluffy frosting. Frost the top and sides of the cake with the frosting.