Slice the ends off the oranges, and discard. Working from the top to the bottom, slice the peel off in strips, to reveal the orange flesh. Cut the white pith from the back of the peel with a sharp knife, and discard. Slice the orange peel into fine julienne strips, put it in a saucepan, cover with cold water, and bring to a boil. Drain, and rinse under cold running water. Repeat this process three times. Blanching the orange peel like this removes much of the bitter taste.
Cut out the sections from the oranges into a bowl, squeezing any juice out of the membrane before discarding. Set aside.
Pour the sugar into a saute pan or large heavy saucepan. Melt the sugar and let it develop a deep amber color, without letting it burn. Pour over 1 cup water/250 ml water and any juice that has pooled around the orange slices. The caramel will seize up, so leave the pan on the heat until the water and juice dissolve into the caramel. Add the drained julienne of zests and boil until they turn translucent, become candy coated and a dark amber color, 5 to 10 minutes. The zests will be sweet and chewy with a faint hint of bitterness and intense orange flavor.
Add about 4 spoonfuls of this caramel with candied orange zest to the fresh orange slices, and toss. Cover, and set aside in a cool place until serving.
(Cool the remaining caramel and orange zest. If too thick, simply thin out with a bit of water to achieve a thick syrup. Store in a glass jar in the refrigerator; it will keep for at least 6 months.)
Serve the oranges with their caramel and candied peel sprinkled with lightly toasted almond slivers and slightly sweetened whipped cream.