Preheat a deep fryer with canola oil to 375 degrees F. You can also use a cast-iron skillet filled halfway with canola oil.
In a skillet set over medium heat, cook the bacon until crispy, about 10 minutes.
In a shallow dish, add the flour and season with some salt and pepper. In a second shallow dish, add the eggs and lightly beat. Dredge the tomato slices in the flour then in the eggs and again in the flour.
Fry the battered green tomato slices until golden brown, 2 to 3 minutes.
In a large skillet set over medium heat, add a tablespoon of the canola oil. Add the fried green tomatoes to the skillet, stacked 2 high. Cover the stack with 2 pieces of the cheese and let melt, about a minute. Repeat with the remaining stacks of tomatoes and cheese, adding another tablespoon of oil halfway through.
Spread some mayonnaise onto both sides of a bun and layer with a stack of fried green tomatoes covered with melted cheese, 2 slices of crispy bacon, lettuce and top with top of the bun. Repeat for the remaining buns and tomato stacks, and then serve hot.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.