Using a small sharp knife or vegetable peeler, cut the peel off an orange in long strips. Cut off any white pith on the peel then dice the strips into tiny blocks.
Combine the white sugar and water in a medium heavy based saucepan over medium heat and stir gently just until the sugar dissolves.
Toss in the chopped orange peel and let it cook on medium low heat until it turns soft and the syrup gets thicker, which should take around 20 minutes.
After that, add in a tablespoon of cold water and let it simmer for an additional minute. Once done, take it off the heat and leave it in the syrup for another 10 minutes to further soften.
Finally, you can spoon the orange peel onto the cooled cupcakes, either with a drizzle of the syrup or without it.
If the sugar solidifies or forms crystals during the cooling process, simply return it to low heat on the stove and warm it up until it transforms back into a syrupy, liquid consistency.