• Preheat oven to 375 degrees. Place the mushrooms on a parchment lined baking sheet, rub with oil and sprinkle with salt on both sides. Place mushrooms gill side down and roast for 30-35 minutes or until slightly golden. Remove from oven and allow to cool. 
  
• Slice the mushroom caps horizontally being careful to make sure to cut directly through so both sides are even. 
• Create a breading station. Place the flour in a deep bowl or pie plate. Whisk 3 of the eggs in a similar sized bowl and the panko in a third bowl.
• For the filling, place the cheeses, onion and garlic powder and one egg in a medium sized bowl and stir to throughly combine. Form the mixture into 4 even sized disks just smaller than the mushrooms. Place a disk of the cheese in between each mushrooms to create a sandwich and press to secure.
• Dredge each stuffed mushroom in the flour, then the whisked egg and finally coating with the panko, pressing to adhere.*
• Heat a large sauté or cast-iron pan with 1 inch of oil over medium high heat (if using a candy thermometer it should read 350 degrees). Fry the burgers on each side for 3-4 minutes or until golden and crisp. Transfer the burgers to a paper towel lined plate to remove excess oil.
•  Place a shroom burger on the bottom of a bun, top with avocado, tomato, lettuce and sauce if desired and top with second bun. 
• * mushroom burgers can be refrigerated overnight at this point. 

For the sauce:

• Place the sauce ingredients in a bowl and stir to combine,