Start off by preheating your oven to 350 degrees Fahrenheit and grease a donut pan.
(Optional) In a small bowl, mix together the water and instant coffee granules and set aside.
In a medium-sized bowl, whisk together the flour, cocoa powder, baking soda and salt. Set aside.
In a separate bowl, whisk together the melted butter, egg, brown sugar, granulated sugar, milk, yogurt and the coffee mixture (if using) until combined.
Add the wet ingredients to the dry ingredients and whisk until a batter forms. It will be thick.
Gently spoon the batter into the donut cavities, or pipe the batter in using a piping bag/ziplock bag with the tip cut off (preferred method). Bake for 11-12 minutes. To test, gently press your finger into the donut. It is ready if the donut bounces back.
Let the donuts cool in the pan for 10 minutes, then remove from the pan and let them finish cooling on a baking sheet.
While the donuts are cooling, break up the candy canes. Put the candy canes into a food processor or blender and pulse them until they are in small pieces. If you do not have a food processor or blender, put them in a ziplock bag and carefully hit the candy canes with the back of a wooden spoon/spatula until they are broken up.
Then, melt the white chocolate chips and oil together in the microwave in 15 second increments, stirring in between each increment. You can also melt the chocolate over the stovetop.
Dip one side of the donut into the melted chocolate, shaking off the excess, and place it on a lined baking sheet. Sprinkle the crushed up candy cane pieces over the glaze.
Leave to set at room temperature for 30 minutes or in the fridge for 10-15 minutes. Enjoy!