Cut a thin slice from the top and bottom of each fruit, then cut vertically through the peel to the fruit, spacing the cuts about 1 inch apart. Remove the peel from each fruit. Reserve fruit for another use.
If you are using the peel to make a candy instead of chopping it, cut each peel section lengthwise into strips 1/4 inch wide. If you will be chopping it, leave the peel sections whole, as they are easier to work with.
In a saucepan, combine 3 quarts of the water and the peel over high heat and bring to a boil. Reduce heat to medium and cook, uncovered, until only 1 inch or so of the water remains in the pan, about 1 hour. Using a slotted spoon, transfer peels to a bowl and set aside. Discard liquid.
In a nonreactive saucepan, combine the remaining 2 cups water with 1 cup of the sugar and bring to a boil over high heat, stirring until sugar dissolves. Remove from heat and stir the still-warm peels into the syrup. Let peels stand for 1 to 2 hours at room temperature. Return pan to low heat and cook peels, stirring occasionally, until they have absorbed all of the syrup, about 30 minutes. The peels will become translucent and amber. During the last stages of cooking, keep a close eye on the peels to prevent scorching.
When peels are ready, remove the pan from the heat and transfer peels to a sheet of waxed paper or parchment paper, arranging them in a single layer. Let dry overnight. To sugar them, place the remaining 1/2 cup sugar on a fresh piece of waxed paper or parchment paper and roll the fruit in it, adding more sugar if needed. Let stand again overnight. Transfer to an airtight container and store in a dry place for up to 2 weeks.
Note: Valencia oranges are the best choice here, as they most resemble the bitter Seville oranges probably used in the original English recipe. Navel oranges will suffice if you don't have Valencias. Use Lisbon or Eureka lemons, as the peel of the Meyer lemon is too thin.
Makes about 4 oz.