Thoroughly wash and dry the oranges, then cut off the tops and bottoms of each. Score the orange peel from top to bottom with a sharp knife to create 4 or 5 large sections.
Carefully remove each section with some of the pith and cut it into ¼-inch sections. Set aside.
Bring five cups of water to a rapid boil in a large saucepan. Add the orange peels and return to a boil for 15 minutes. Drain and rinse the peels thoroughly before shaking out the excess liquid. Set aside.
Add one cup of water and two cups of sugar to the same saucepan and set the heat to medium. Stir the mixture occasionally until the sugar is thoroughly dissolved.
Add the boiled orange peels and increase heat to medium-high to boil. Once boiling, immediately reduce heat to medium-low and simmer, uncovered, for 40-45 minutes.
Remove from the heat and drain, reserving both the orange-flavored syrup and the orange peels*. Transfer the peels to a wire rack set over a rimmed baking sheet. Set aside to dry for 12 hours to overnight.
Once the peels are mostly dry, but still a bit tacky, add the remaining sugar to a large Ziploc storage bag and add the peels a few at a time. Seal and shake the bag carefully until the peels are uniformly coated in sugar. Repeat this process with the remaining peels until all are uniformly coated in sugar.
Serve the candied peels immediately as a snack, or use as a delicious garnish for ice cream, cupcakes, or cakes. They also make a wonderful addition to homemade cannoli filling. Unused orange peels can be stored in an airtight container for up to a week. Enjoy!