Cut the top and bottom of each orange with a sharp knife. Make four vertical incisions into both oranges' peels and piths without cutting into the fruit. Separate each fourth of the peel, including the pith, from the fruit using your fingers.
Put orange peel slices in a medium saucepan with enough cold water to cover them by an inch. After boiling on high, lower heat to a simmer and cook for 15 minutes. Drain peels. If your fruit is bitter, repeat up to twice (see remark).
Clear the saucepan. Heat sugar and 2 cups water on medium. The sugar will dissolve into syrup and boil. When the syrup boils, gently add the orange peels and lower the heat. The peels should simmer gently, so adjust the heat as needed.
Remove the pan from heat. Carefully drain the peels over a heatproof basin when the syrup stops boiling. See note on syrup reuse.Put superfine sugar in a shallow basin or rimmed sheet pan.
Place candied orange peels in a single layer on a parchment-lined sheet pan or nonstick wire rack. Leave them uncovered at room temperature overnight or for 12 hours to dry. When they no longer feel sticky and don't stay together, they're ready.