Line a clean clay or plastic flowerpot (6-inch diameter at the bottom, 4 inches deep and 8-inch diameter at the top) with heavy duty foil, pressing it to the base and sides. Brush the foil with oil.
In a heavy medium saucepan, bring 3/4 cup water, the sugar and corn syrup to a boil over high heat. Cook, swirling the pan, until the sugar is dissolved, 1 to 2 minutes. Cover and boil for 4 minutes until thick and syrupy. Uncover and cook until the caramel begins to turn amber, 8 to 11 minutes. Immediately remove the pan from the heat and swirl to color evenly (the caramel will continue to darken). Place the pan on a folded towel next to the lined flowerpot.
Using tongs, dip the doughnut holes into the caramel to coat about halfway; beginning at the bottom edge, arrange in a ring against the sides of the lined flowerpot, so that the caramel coated parts touch each other. Continue dipping the doughnut holes, tilting the flowerpot as necessary, and placing and stacking them snugly together until you have a stack of three full rings resting against the foil. Let cool for about 10 minutes.
Invert the confection onto a platter, remove the flowerpot and carefully peel off the foil and discard. Fill the hollow tower base with uncoated doughnut holes. Dip more doughnut holes in the caramel and place on the top ring of doughnut holes. Build up the tower by continuing in this way, making each doughnut-hole ring smaller than the one beneath it until you come to a point, forming a pyramid-shaped tower. If the caramel becomes too hard for dipping, reheat it over medium-low heat until reliquified.
Using a fork, drizzle any remaining caramel over the tower.