Pre-heat the oven to 375°F.
Place the potato in a small bowl with enough water to cover it and microwave at high power until tender, about 8 minutes. Drain, add the milk and mash with a fork; let cool. Mix in the eggs.
In a medium size, ovenproof skillet, heat the EVOO, two turns of the pan, over medium heat. Add the zucchini and cook until tender, about 5 minutes. Add the potato mixture and stir to combine. Bake until set, about 10 minutes. Sprinkle the cheese on top and bake until melted, about 2 minutes more. Let cool, then cut into wedges. Garnish with basil, if desired