In a bowl combine mayonnaise, sour cream, cajun seasoning, vinegar and Dijon mustard. Chill until burgers are finished.
Cook bacon in a pan over medium heat. Transfer to a plate. Reserve pan drippings. Remove from heat while you prep the tomatoes.
Place the flour on a plate. Whisk the egg and milk together in a bowl. Place panko bread crumbs on another plate.
Season the green tomatoes with salt and pepper on both sides. Dredge the tomatoes in the flour. Then dip in the egg/milk wash then dredge in the panko bread crumbs. Repeat until all tomatoes are coated.
Return the pan with bacon drippings to the heat. Drop a couple panko bread crumbs in, if they sizzle then it's ready to go. Fry the tomatoes 2 - 3 minutes per side or until golden brown. Transfer to a plate. Cover to keep warm.
In the same pan, cook the hamburger patties. You can also grill them if you prefer.
Turn on the oven broiler and broil hamburger buns 1 minute or until golden.
Spread cajun mayonnaise over the top bun. Place lettuce on the bottom bun. Top with ground beef patties. Top each burger with a couple slices of bacon and 2 fried green tomatoes. Serve.