For the pesto: In a food processor, blend all pesto ingredients together except the olive oil. After everything is combined, drizzle in olive oil while the food processor is running. Taste and adjust. If its bland, add some salt and pepper. If it's too tangy, add more honey or sweetener, if it's not tangy enough add more vinegar or lemon juice. Set aside.

For the caramelized onions: In a medium sized skillet, heat oil over medium heat. Add onions and salt and saute until translucent. Add balsamic and honey (or agave) and saute until they cook down and are brown and caramelized (about 4 more minutes). Set aside.

For the balsamic mushrooms: In a separate medium sized skillet (or wipe out the one from the onions), heat oil over medium heat. Add mushrooms and a few pinches of salt and cook down for 5 minutes or so, careful to not burn them to the bottom of the pan. Add a splash of balsamic to deglaze. If mushrooms are sticking, add a little more oil, or a few splashes of water to loosen them up. Cook until they're browned and wilted down. Set aside.

Assemble the sandwiches: I actually grilled these open faced - the side with the cheese longer (so the cheese could sufficiently melt), the side with the pesto, not as long (so the pesto wouldn't dry out or become bitter), and then put the 2 sides together, pressing down gently to get them to stick.