Preheat the oven to 350°F. Grease a 9-inch round cake pan with cooking spray. Line the bottom with a round of parchment paper and lightly spray again.
In a large bowl, add the granulated sugar, Greek yogurt, oil, eggs, and vanilla extract. Whisk together until well combined.
Add the flour, cocoa, baking powder, espresso powder, and salt use a spatula to stir until just combined. Don’t over mix.
Pour the batter into the prepared pan and bake for 30 to 35 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and let cool in the pan for 15 minutes. Then, invert it onto a wire rack, flip it upright, remove the parchment, and let cool completely.
While the cake is cooling, make the frosting. In the bowl of a stand mixer fitted with the paddle attachment (or using a large bowl and hand mixer), beat the softened butter on medium speed until smooth and creamy, about 1 minute. Add the Greek yogurt, vanilla extract, and salt. Beat until fully combined and smooth, scraping down the sides of the bowl, as needed. In a separate bowl, whisk together the confectioners’ sugar and cocoa powder to remove any lumps. With the mixer on low speed, gradually add the sugar mixture to the butter mixture. Once incorporated, increase the speed to medium and beat until the frosting is smooth, creamy, and spreadable.
Spread the frosting over the cooled cake. You might have a little leftover frosting, depending on how much frosting you like. Serve the cake with berries, if desired.