To make the cinnamon topping, melt the butter in a small saucepan. Stir in the cinnamon, brown sugar, milk, and cornstarch.
Heat just until it begins to boil. Remove from the heat and stir in the vanilla.
Pour the cinnamon topping evenly into each well of your well greased donut pan.
To make the donuts. reheat the oven to 325 degrees. Lightly grease a donut pan.
In a large bowl, whisk together the flour, sugar, baking powder, nutmeg, cinnamon, and salt.
In a small bowl, stir together the butter milk, egg, and oil.
Add the wet ingredients to the dry and stir with a wooden spoon until fully incorporated.
Drop spoonfuls of the batter into the donut pan over the cinnamon topping and bake for 10 minutes or until lightly browned and cooked through.
Remove from the oven and cool in the pan for two minutes before transferring to a wire rack. Some of the cinnamon topping will likely be left in your donut pan, but a good portion of it will have transferred to your donuts.
Cool donuts before glazing.
To make the glaze. whisk together the powdered sugar and cream until smooth. Spoon into a baggie and cut off a small corner of the bag. Pipe the glaze onto the donuts.