Start by heating the oven to 175°C (350°F). Prepare a 9-inch cake pan by greasing it well, then line the base with parchment paper so the cake doesn’t stick.
In a large bowl, add the Greek yogurt, eggs, sunflower oil, sugar, and vanilla extract. Whisk everything together until the mixture looks smooth and evenly combined.
In a separate bowl, sift the flour, cocoa powder, baking powder, and salt. This helps remove lumps and keeps the cake light. Slowly add the dry ingredients to the wet mixture, folding gently until just combined. Stop mixing as soon as you no longer see dry flour to avoid making the cake dense. Fold in the chocolate chips carefully.
Pour the batter into the prepared pan and use a spatula to level the surface. Place the pan in the oven and bake for 35–40 minutes. The cake is ready when a toothpick inserted into the center comes out clean or with just a few crumbs.
While the cake is baking, make the frosting. Beat the butter in a bowl until soft and creamy. Gradually add the sifted icing sugar and cocoa powder, mixing well after each addition. Pour in the milk and continue beating until the frosting becomes smooth and fluffy.
Once the cake has finished baking, remove it from the oven and allow it to cool completely. After it has cooled, spread the frosting evenly over the top. Slice the cake and serve.