Pour the vegetable oil into a sauce pan and place on stove over medium-high heat.
Remove the biscuits from the can and lay them on a cutting board. Using a 1 inch round cookie cutter, cut circles from each biscuit. You should be able to get 4 circles from each biscuit. If you don't have a cookie cutter, a bottle cap (such as one from a bottle of olive oil) would work as well.
Carefully place 4-6 of the donut rounds into the oil. Once one side is golden brown, use tongs to flip and fry the other side. When finished, remove from oil and place on a plate to cool.
To make the glaze, add the milk, vanilla and powdered sugar to a shallow bowl, and mix until combined.
In a second shallow bowl, add the sweetened coconut shreds.
Dip each donut round into the glaze and then roll it around in the coconut until covered. Place on parchment paper to set.