Preheat the oven to 160 ºC and line an 8 inch square baking pan with parchment paper.
Mix the yoghurt and sugar till the sugar dissolves completely. THIS IS IMPORTANT, please do not skip this step.
In a separate microwave safe bowl add the chocolate and in 20 second increments, melt completely.
Mix together the softened butter and the yoghurt mixture till well combined and smooth, now add the melted chocolate and stir evenly. Make sure the mixture is smooth. Now add the coffee and vanilla and stir to combine.
Sift in the flour, cornflour, cocoa powder, baking powder and salt. Whisk to combine, do not overmix.
Pour the batter into the prepared baking tin and smooth out the top.
Bake in the pre-heated oven at 160C for about 30 minutes, or until an inserted toothpick comes out with some half-baked batter and many moist crumbs attached.
Let the brownies cool completely at room temperature before slicing and serving.