In a medium saucepan, place 3 cups water and the walnuts and bring to a boil. Add the sugar and boil for 3 minutes. Turn off the heat and let the walnuts soak in the sugar syrup for 2 hours. Drain well and let the walnuts dry for 2 hours. (If you want to hasten the drying process, spread out on a cookie sheet and place in a 350°F oven for 3 minutes.)

Heat the vegetable oil to 350°F. And deep-fry the walnuts until they are brown, about 1 minute. Be careful not to burn the walnuts. Remove the walnuts and cool completely. Store in an airtight container.