Preheat your broiler, on a foil lined baking sheet place the poblano cut side down, tomato, garlic unpeeled, and the onion. Broil until there is some char on the veggies, about 8 to 10 minutes. While they are broiling season the meat with the cajun seasoning and form into 4 equal patties a little larger then your bun.

Heat a large cast iron skillet over medium high and add just a touch of oil. Place the burgers down and cook them for 4 minutes without moving them. Flip them over, top with cheese and cook for another 3 to 4 minutes.

While the burgers are cooking the veggies should be done and cooled off a bit. Peel the garlic and chop it up with the tomatoes and onions and season with a little salt and pepper, set aside. Peel any charred tough skin off the poblanos now as well. Turn off the broiler and place the buns the oven in to warm up from the residual heat, check on them every now and again to make sure they don't get too crispy.

Open your buns and build the sandwich. Bottom bun, burger with cheese, mayo, poblano half, tomato mixture, bun top. Enjoy!!