Heat the butter and oil in a heavy bottomed frying pan (I used a cast iron skillet) over medium low heat, until hot, but not smoking.
Working one at a time, dip each slice in seasoned flour, then egg, then 'Parmesan', pressing the cheese onto all the sides to help it adhere, before adding it to the hot pan.
Fry the slices, keeping the heat medium-low, turning once. When the cheese is crisp and golden and the mushroom is hot and tender all the way through, they are ready - about 5 minutes per side.
Transfer to paper towels to drain the excess fat, then serve immediately with crusty sourdough rolls and whatever burger toppings and garnishes take your fancy.