Combine the garlic and oil in a large bowl, warming it in the microwave until the garlic is fragrant, about 1 minute. Transfer 5 tablespoons of the oil (leaving the garlic in the bowl) to the baking sheet, coating it well.
Add the potatoes to the bowl with the garlic mixture and toss to coat.
Wrap the bowl tightly in plastic wrap and microwave on high power until the potatoes are translucent around the edges, 3 to 6 minutes, shaking the bowl to redistribute the potatoes halfway through cooking.
Combine the cornstarch, salt, pepper, garlic powder, and cayenne in a small bowl. Sprinkle over the hot potatoes and toss well to coat.
Arrange the potatoes in a single layer on the prepared baking sheet.
Bake, turning once, until deep golden brown and crisp, 30 to 40 minutes. Serve with your favorite condiment.