Mix together the nondairy milk, orange juice, zest, sugar, and olive oil.
Sift together the flour, cornstarch, baking soda, and salt and add to the olive oil mixture. Fold together gently, being careful not to overmix.
Scoop the batter into the wells of a greased donut pan, filling about 3/4 of the way full. Bake for 15-20 minutes until the donuts are golden brown on the edges.
To make the glaze - Mix together the powdered sugar, zest, and juice and stir until completely smooth. Drizzle over the cooled donuts, or dip the donuts carefully (the glaze sets very quickly, so if you choose to dip be careful not to rip the donuts!).