1. With sharp knife, cut a slice off tops and bottoms of oranges. Score peels in four sections; pry peels off. Save fruit for another use.
2. With spoon, carefully scrape as much of white pith as possible from inside of peels. Combine peels and 6 cups water in heavy saucepan. Bring to boiling; simmer 10 minutes.
3. Drain water; add another 6 cups fresh water. Simmer for 10 minutes. Drain and replace water again; simmer for 20 to 25 minutes or until peels are tender.
4. Drain peels in a colander. When peels are cool enough to handle, cut each peel into four 1/2-inch-wide strips (for a total of 48 strips).
5. In same saucepan, combine 1-1/2 cups water, corn syrup and 1 cup of the sugar. Bring to boiling; boil for 3 minutes. Add peels; reduce heat to medium and cook, covered, until the peels look translucent, for about 20 minutes. Uncover pan; continue to cook until the sugar syrup reduces to about 1/4 cup, 20 to 25 minutes.
6. Place wire rack over 15 x 10 x 1-inch jelly-roll pan. With tongs or fork, transfer peels to rack to drain slightly.
7. Spread the remaining 1/2 cup granulated sugar in second jelly-roll pan. While still warm, transfer peels to sugar-filled pan; roll to coat. Return to rack. Dry thoroughly, 2 hours.
8. In top of double boiler over simmering water or in microwave-safe bowl in microwave oven, melt chocolate and shortening until smooth and good dipping consistency. Hold each peel by one end; dip in chocolate. Place on waxed paper. Let cool until set.