Remove the stems of the figs and place into a food processor. Pulse a few times until well pulverized. Mix into the mayonnaise recipe and place in the refrigerator.
Heat the balsamic vinegar in a saucepan on medium high heat for 3-4 minutes or until the quantity is reduced by approximately half and slight thickened into a syrup. Pour into a small cup and place it in the refrigerator to cool down. (*Be careful not to overcook it, otherwise it will be too thick when cooled).
Preheat your grill or grill pan to medium heat. Season your burger patties with salt, pepper and garlic powder and place on the grill. Cook for 4-5 minutes each side, or until the meat reaches your desired temperature.
Place the pineapple slices on the upper shelf of your grill, away from the high heat. Flip them when you flip your burgers. Alternatively, if you don't have an upper shelf you can place them on the main grill (or grill pan) but watch that you don't overcook them. You'll probably need to flip them in half the time.
While the meat is cooking, separate the arugula between four plates. Slice the figs into quarters and divide equally onto the plates. Slice a half an avocado onto each plate.
Mix the olive oil and balsamic vinegar together. Drizzle onto the salads.
At this point, your cooked balsamic (in the refrigerator) should be cooled down. Stir this into your fig mayonnaise and set aside.
Remove the burgers and pineapple from the grill when cooked. Place one burger on each bowl of greens. Spread a dollop of fig mayonnaise on top of. Then top with a pineapple slice.
Leftover fig mayonnaise can be kept in the refrigerator for 4-5 days.