Heat oil in a small saucepan over medium heat.  Add onion and saute, stirring occasionally, until browned, about 10 minutes.  Add the fig preserves and balsamic vinegar; turn heat to low and cook, stirring frequently, until onions turn a deep brown, 5-10 more minutes.  Remove pan from heat and let cool slightly.

Spoon fig-onion jam on two pieces of bread and layer turkey, arugula and fig slices, if using, on top.  Top each sandwich with remaining pieces of bread.  Slice in half before serving.  Store any remaining jam in an airtight container in the refrigerator for up to two weeks.