Using a sharp knife, cut the peel off the oranges, taking as much as possible to get ride of most of the pith. The pitch can be very bitter. Cut the peel into 1/4-inch strips.
In a large saucepan, combine the peels with water by 2 inches. Bring to a boil over high heat, then reduce the heat to simmer. Continue to simmer peels, uncovered, for about 1 hour. There should only be about 1 inch of water remaining, and the peels should be soft and somewhat transparent. Drain the peels.
In another saucepan, bring 4 cups of water and 2 cups of sugar to a boil. Stir to dissolve the sugar. This should take about 3 to 4 minutes. Remove from heat and stir in the drained peels. Let stand at room temperature for 6 to 8 hours.
Return the pan to low heat and bring to a simmer. Cook for about 30 minutes or until the peels have absorbed most of the syrup. Watch carefully to prevent burning.
Remove the peels from the saucepan and lay them out individually on wax paper. Allow them to dry for about 12 hours. They will still be a little wet, but not soggy.
Place about 1/2 cup of sugar in a bowl and roll the orange peels in the sugar until they are fully coated. Arrange peels in a single layer on a piece of wax paper and let them dry. To hasten drying, arrange peels on a sheet pan and place in the oven on the lowest setting. Keep the door cracked and leave them to dry for a couple of hours.
Store in layers separated by waxed paper in an airtight container. Try candied orange peel dipped in chocolate for an extra tasty treat. Enjoy! Happy cooking!