Wash the oranges well, then slice off the top and bottom. Using a channel peeler or sharp knife, remove the peel in long strips. If using whole peels, cut them into thin, even strips. Use a sharp knife to remove most of the white pith, leaving a thin layer attached. Too much pith can make the candied peels bitter. Cut the peels into thin strips, about ΒΌ inch wide. Try to keep them fairly even so they cook at the same rate.
Place the orange peels in a pot of water and bring to a boil. Simmer for about 10 minutes, then drain. Repeat this process one more time using fresh water. This step is important for removing excess bitterness from the citrus.
In the same pot, combine equal parts sugar and water. Add the boiled peels, stir thoroughly and simmer on low heat for 45 to 60 minutes, until the peels look translucent and glossy. Stir occasionally to prevent sticking.
Using a slotted spoon, transfer the candied orange peels to a wire rack set over a baking sheet. Let them dry at room temperature for several hours, or overnight, until no longer sticky.