Place the mushrooms into a plastic bag, set them aside.
In a small mixing bowl, whisk together the balsamic vinegar, olive oil, pesto, salt, and black pepper.
Pour into the bag, zip it, and toss the rooms in the marinade.
Marinade for 30 minutes on the counter. Toss every few minutes to make sure that the mushrooms are evenly coated in the marinade.
Preheat the air fryer to 370 degrees F.
Place the mushrooms, stem side down into the air fryer's basket, not touching.
Air fry for 7 minutes, until mushrooms are tender. You may need to do this in batches.
While the mushroom burgers are air frying, prepare the sauce. Mix the mayonnaise and pesto in a small bowl.
To Plate: Place the mayonnaise on the bottom bun, top with the cooked portobello mushroom, and then add a slice of tomato and a few leaves of basil.