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2 Preheat oven to 375°F. 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. 
3 Slice the mushroom caps horizontally being careful to make sure to cut directly through so both sides are even. 
13 For the cheese 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. Refrigerate until ready to use.
4 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.
6 Dredge each stuffed mushroom in the flour, then the whisked eggs and finally coating with the panko, pressing to adhere.
7 Heat a large sauté or cast-iron pan with 1/2 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.
14 Make the faux ShackSauce. Place the sauce ingredients in a bowl and stir to combine.
8 Place a shroom burger on the bottom of a bun, top with avocado slices, tomato, lettuce and ShackSauce (if desired) then top with second bun.