Remove zest and pith (the white part) from the oranges with a sharp pairing knife in large strips.
Slice the strips into 1/2-inch thick widths and place in a large pot. Cover with cold water and bring to a boil. Once boiling, drain and repeat two more times.
Return to the pot and add 4 cups sugar and 4 cups water. Bring to a boil and cook vigorously, stirring occasionally, until syrup is thick and peel looks translucent, about an hour. If syrup is bubbling violently, turn down heat.
Carefully drain peel in a fine strainer set over a heat-proof bowl (save this syrup for cocktails).
Put 3 cups sugar in a medium bowl. Place 1/3 of the peel in the bowl and toss in the sugar until thoroughly coated. Spread peel out on a parchment lined baking sheet and repeat with remaining peel, doing 1/3 at a time.
When dry, store in a tightly-covered container for up to 2 weeks.