To make the artichokes, toss the artichokes in the flour and shake off any excess.
Heat the oil in a heavy-bottomed pan (CAUTION: hot oil can be dangerous, do not leave unattended). When hot add the artichokes and fry until crisp and golden. Remove from the oil with a slotted spoon and drain on kitchen paper.
To make the vinaigrette, place all the vinaigrette ingredients into a bowl and mix together.
To serve, arrange the artichokes and cooked mussels on a plate, season, and spoon over the vinaigrette.