Preheat the oven to 325 degrees. Lightly grease a donut pan.
In a large bowl, whisk together the flour, sugar, baking powder, and salt.
In a small bowl, stir together the buttermilk, egg, and oil.
Add the wet ingredients to the dry and stir with a wooden spoon until combined. Stir in the melted white chocolate.
Fill the donut pan and bake for 8-10 minutes or until lightly browned and cooked through.
Remove from the oven and cool in the pan for a few minutes before transferring to a wire rack.
To make the glaze:
Add the boiling water and espresso powder to a small bowl and whisk until combined. Whisk in the powdered sugar, vanilla, and salt. The glaze will be thin.
Dip the donuts in the glaze and set on a cooling rack for 10-15 minutes.
For the drizzle:
Melt together the white chocolate and milk in a microwave safe bowl or in a double boiler.
Use a spoon to drizzle the white chocolate over the donuts.