Finely grate the zest (use a rasp-style grater if you have one) from one of the oranges to get 2 teaspoons zest. Cut the tops and bottoms off each orange, being sure to cut into some of the flesh; reserve th tops and bottoms. Cut the peel off the sides, exposing the flesh by cutting under the pithy membrane. Discard the peels cut from the sides. Cut each orange in half vertically, trim out the pithy core, and then slice each piece crosswise into 1/4-inch half moons. Arrange the slices on a large, shallow serving dish or deep platter.

Combine the zest and crystallized ginger on a cutting board and chop them together until they're well mixed. Scatter the ginger and zest evenly over the oranges.

Put 2 tablespoons water in a small, heavy saucepan and pour the sugar on top. Bring to a boil over high heat, lower the heat to medium high, and boil without stirring until the syrup has turned a deep medium brown, 5 to 8 minutes. Watch the pan carefully during the last few minutes, as the caramel goes quickly from brown to burnt. Using a heavy pot holder to hold the pan, immediately drizzle the caramel over the oranges, getting a bit of caramel on each slice. Scatter the mint over the oranges. Squeeze the juice from the reserved ends of the oranges over all.