Preheat the oven to 350˚F. Grease and flour a 9-inch cake pan. Set aside.
In a large bowl, whisk together the oil, yogurt, eggs and espresso. Once evenly combined, stir in the flour, sugar, baking powder and chopped walnuts. Pour the batter into your prepared pan and bake in the oven for 25 minutes, or until a toothpick inserted comes out clean.
Allow the cake to cool in the pan for a few minutes and then transfer to a wire rack to cool completely.
While the cake is cooling, make the buttercream frosting. In the bowl of a stand mixer fitted with the whisk attachment or using an electric hand mixer, beat the butter and sugar together until pale and fluffy, about 5 minutes. Slowly add in the espresso until it is completely incorporated.
Frost the top of the cake and decorate with walnut pieces as you like.