Cut the top and bottom off each orange, and score the skin into quarters. Remove the peel, leaving most of the pith on the fruit. Store oranges in a plastic bag for other use. Trim excess pith off the peels. Slice peels lengthwise into 1/4-inch strips.
Place the strips into a large saucepan and cover with cold water. Bring to a boil, then drain. Repeat twice more.
In the same pan, bring sugar and 4 cups water to a boil, stirring occasionally until sugar has dissolved. Add strips to the boiling syrup, reduce heat to medium-low, and simmer gently, without stirring, until strips are translucent, about 45 minutes to 1 hour. Remove from heat and let strips cool in syrup.
Using a slotted spoon, transfer strips to a wire rack placed on a rimmed baking sheet. Wipe off excess syrup with paper towels, then roll strips in sugar. Arrange in a single layer, on a wire rack, and let dry for 4-5 hours. Candied peels can be stored in an airtight container at room temperature for up to 2 weeks.
Cook's Note: Do not discard orange syrup, it can be used to sweeten tea, etc. For an extra treat, dip one end of the candied peel in melted chocolate and allow to cool on a baking sheet lined with parchment. Wrap in decorative plastic bags for gift giving.