Using a sharp knife, carefully slice off thin strips of just the outer orange peel, trying not to cut off too much of the bitter white pith along with it. You won't need the orange pulp for this recipe, so you can eat it or juice it.
Place all the orange peel strips in a saucepan, and cover with water. Bring to a boil, and boil for 20 minutes. Drain and set aside.
Measure 1 cup of clean water into the saucepan and add 2 cups granulated sugar. Over medium heat, bring the syrup to a boil, and continue to boil until the syrup reaches 230 degrees F. Return the orange peel to the syrup, and simmer for 5 minutes. Drain. (If you like, you can save and strain the orange-infused syrup to use in cocktails, or other recipes.)
Before the drained orange peels dry, spread them out onto a parchment-lined baking sheet, and sprinkle with the remaining 1/4 cup granulated sugar, tossing until all the pieces are well coated in sugar. Let cool completely, and then store the candied orange peel in an airtight container.
Kept in an airtight container, candied orange peel will keep indefinitely.