Cook peels in a large pot of boiling water for 15 minutes; drain, rinse, then drain again.

Bring 3 cups sugar and 3 cups water to a boil in a medium saucepan, stirring to dissolve sugar. Add peels, reduce heat, and simmer until very soft, about 40–45 minutes; drain.

Toss peels with remaining 1 cup sugar on a rimmed baking sheet to coat. Transfer peels to a large sheet of foil and let sit until dry, 1–2 days.

Do Ahead: Orange peels can be candied 1 month ahead. Store airtight at room temperature, or freeze up to 2 months.