Clean and remove the stems from the Portobello mushrooms. Cover the mushroom caps with salt and oil and place them into the preheated to 375°F (190°C) oven for 30 minutes. After, When the mushrooms are baked, take them out of the oven, and pat them dry with a paper towel. Let them cool down a little bit.
Prepare the filling. Mix the processed cheese, grated Cheddar cheese, smoked paprika, and garlic powder together. Set aside in the fridge while mushrooms are being baked.
Stuff one cap with the cheese filing and cover it with the second cap.
Prepare the breading. Whisking the egg in one bowl. In a separate bowl, mix the flour and salt. In the third bowl, place the panko breadcrumbs.
Cover the stuffed mushroom with the flour first. Then dip it into the beaten egg, and then coat it with the breadcrumb mixture.
Heat oil in a pan or skillet and fry the breaded mushrooms until golden brown and crispy. Drain them on a paper towel to remove excess oil.
For the sauce, combine mayo, Dijon mustard, ketchup, pickle brine, cayenne pepper, and garlic powder in a bowl. Mix well. Taste and adjust any more ingredients according to your taste.
Assemble the burger. Spread some sauce on the fried bun, place lettuce leaves and the tomato slices. Then place the cooked mushroom. Drizzle with some more sauce and cover with the second bun. Enjoy!