Preheat oven to 170c/325f Lightly oil two, 6-piece doughnut ring tins with vegetable oil or spray.
In a large bowl, mix the flour, sugar, baking powder, baking soda, and salt until combined. Add in the egg, yogurt, coconut oil and milk. Mix, using a spatula until everything is just combined.
Spoon the doughnut batter into a piping bag (no tip required) or a sandwich bag with the corner cut off. You want the hole to be approx. ¾”. This makes it easier to fill the doughnut tins. Pipe the batter into each tin.
Place the doughnuts in the oven and bake for 12-14 minutes, until an inserted skewer comes out clean.
Take the doughnuts out of the oven, leave to cool for 10 minutes in the tray, before removing and cooling for another 5 minutes on a cooling rack.
Break up the dark and white chocolate into small chunks and place into separate bowls. Melt in the microwave in 30-second bursts, stirring in between each burst, until fully melted (or alternatively, you can melt over a bain marie).
Spoon the white chocolate into a piping bag with a fine tip (or use a sandwich bag and cut a tiny bit off the corner).
Dip one of the doughnuts, smooth-side-down into the dark chocolate. Let the excess drip off, then turn over a place on the cooling rack. Take your piping bag and draw 3-4 concentric circles onto the doughnut using the white chocolate (see image in post). Use a toothpick or cocktail stick to drag lines from the centre of the doughnut to the outside. Do this all the way around, until you have a spider web effect.
Repeat with the rest of the doughnuts. Serve immediately (they will look shiny until the chocolate sets), or carefully cover and store at room temperature for up to one day.