Melt the butter and set to one side.
Pre-heat the oven to 175ºC (350℉) and prepare a muffin tin by greasing or using muffin cases (see note 1)
Add the butter, sugar, eggs, coffee and vanilla extract to a large bowl and whisk until everything is combined (you can use a stand mixer).
In a separate bowl, mix the flour, cocoa, baking soda, and baking powder together.
In a third bowl, mix the milk and Greek yoghurt together.
Gradually add around a third of the dry ingredients to the butter mixture, stir until just combined, and then a third of the Greek yoghurt mixture, again stirring to combine.
Repeat until you have used all the ingredients.
Finally, chop the white chocolate into chunks and stir in half.
Pour or spoon into the muffin cases and sprinkle over the remaining chocolate.
Bake for 20-25 minutes (depending on the size of the muffins). They are ready when an inserted skewer comes out clean. Allow to cool for a while before eating warm.