In a bowl, whisk together flour, baking powder and salt. Set aside. In another bowl, beat together the butter and sugar with an electric mixer until light and fluffy. Add in the eggs, beating after each addition. Mix in the yoghurt until smooth. Whisk in the dry ingredients until just combined.
Remove about 2/3 to 3/4 cup of batter and place in a separate bowl. Add the cocoa powder and mix until smooth. Pour enough of the light batter to evenly coat the bottom of your greased pan. Then add the chocolate batter and light batter in a checkerboard pattern. Once all the batter has been added, take a knife or a toothpick and run it through the batter, swirling it around (or simply add the light batter, then add the chocolate batter in spots, grab a fork and move it around a few times in the batter).
Bake for about 45 minutes at 180°C/350°F, or until a toothpick inserted into the center comes out clean. Cool in the pan for 5 minutes, before placing on a cooling rack to cool completely.