In a medium bowl, combine Worcestershire sauce and water to create the marinade. Place Portobello mushroom caps in zipper-seal bag (quart or gallon size). Pour marinade into bag and seal shut. Make sure mushrooms are coated and let marinate for two hours.
When mushrooms are done marinating, set up a breading station:
In a small bowl, whisk eggs. Set up a separate bowl with the flour. Set out a third bowl and fill it with the panko breadcrumbs. Coat each Portobello cap first with flour, then coat with egg, then coat with panko and set aside.
Preheat air fryer to 350°F according to your model’s directions.
According to your air fryer size, fry 1 to 2 breaded Portobello mushrooms at a time for about 15 minutes, or until crispy and cooked through. The mushrooms will weep moisture but stay tender. Check mushrooms about halfway through for doneness and adjust cooking time accordingly.
While mushrooms are cooking, heat a small amount of olive oil in a medium pan. Sauté onion slices about 5 minutes until caramelized. Set aside.
After a batch of mushrooms is done in the air fryer, top each with 2 crisscrossed slices of Cooper® cheese. Air fry for a minute longer to melt the cheese.
Assemble your burgers:
On the bottom of each kaiser roll add a layer of lettuce, tomato, sautéed onions, and pickles (if desired). Place each hot and crispy fried Portobello burger on top of the fixings. Cap off each burger with the tops of the kaiser rolls.
*Consuming raw or undercooked meats, poultry, seafood, shellfish, or eggs may increase your risk of foodborne illness.