Cut 1 thin slice from the middle of the orange and cut it into little triangles; reserve.
Juice the remaining orange.
In a large skillet that has a lid, mix the minced basil, oil, pepper, mussels, water, shallots, orange juice and half the grated rind. Cover the pan and bring to a boil and steam for a few minutes until the mussels open.
Remove the mussels with a slotted spoon and toss the ones that didn't open.
Place them on plates lined with fresh basil leaves. Garnish with orange triangles. Sprinkle the remaining orange rind on top.
Pour the cooking broth into a small dishes, to dip mussels into.