PORTLAND, Maine—Around here, you can find "Maine Potato Candy"—mashed potatoes rolled in coconut and dipped in chocolate—and potato donuts. A popular county fair offers wrestling matches in a vat of potatoes. In a state where spuds are the top agricultural product, locals can't get enough of them, even at schools.

"We've got to have potatoes—our children are used to potatoes," says Louise Bray, food-service director for Caribou, Maine, public schools. She regularly serves hash browns for breakfast, plus mashed potatoes, "Maine...