Using the Hand Mixer on the third speed setting, whisk the butter with the two types of sugar until pale and fluffy. Next, add one egg at a time, alternating with a spoon of yogurt. Pour in the espresso and keep mixing to combine.
Slowly add in the flour while continuing to whisk. The mixture should be firm and frothy.
Grease a bundt tin and pour half the mixture to the bottom.
Form a groove in the mixture with the back of a spoon and pour the cream cheese mixture into the well. Cover with the remaining part of the cake mix.