• Sauté red onion with olive oil in pan over low heat until translucent and tender.  Remove from heat.
• Fire up the grill to high for direct heat grilling. Clean and oil your grates.
• Season the chicken with salt and pepper.
• Place the breast on the hottest part of the grill 2 minutes.
• Using tongs, lift each breast, rotate 45 degrees and then place them back on the grill.
• After 2 to 4 minutes, lift the chicken breasts with tongs and flip them over.
• Grill for 2 more minutes and then rotate again 45 degrees to make our grill marks on this side.
• Continue grilling for another 1 to 2 minutes until juices run clear and then add the cheese.  Cook until cheese is melted, about 1 minute.  Remove from grill and let rest.
• Toast buns over direct heat until brown.
• Assemble sandwich with spring mix on the buns, then add chicken and onions.  Add reduced balsamic vinegar as a final touch.

For the balsamic vinegar reduction:

• Place three cups balsamic vinegar to a non-reactive,  heavy-bottomed pot, preferably stainless steal.  Heat on low, until it just begins to simmer.  Reduce until it thickens to the consistency of chocolate syrup, or to desired consistency, about 2 to 2 1/2 hours.  Be careful not to burn near the end of the thickening process.
• To test the consistency, drizzle a bit onto a plate and then check how sticky it is.  If  it is too thick, add a little water to the pot, stir it up, and retest.
• If you have a side burner on the grill, this is a great item for outdoor cooking.  Otherwise, it will likely stink up the whole house.  But it is worth it.  This stuff is the nectar of the vinegar gods.  Enjoy.