Preheat a gas grill or large grill pan to medium high heat.
In a medium mixing bowl, stir together the shredded extra sharp cheddar cheese, mayonnaise, ¼ teaspoon salt, 1/8 teaspoon pepper, pimento, red onion and garlic powder.
On a large foil lined, rimmed cookie sheet place an oven safe metal cooling rack. Place the bacon strips on top of the cooling rack and place the whole pan in a cold oven. Turn the oven on to 400 degrees and allow the bacon slices to cook for 15-17 minutes. While the bacon is cooking, whisk together the brown sugar and cayenne pepper in a small mixing bowl. Remove bacon from the oven and flip each slice over. Sprinkle the brown sugar mixture evenly over all of the bacon slices. Return the pan to the oven to finish cooking for 8-10 minutes or until bacon is fully cooked and the sugar crust is nice and bubbly.
While the bacon is cooking, grill the green tomatoes and buns. Brush the tomato slices with oil and sprinkle with ¼ teaspoon salt and 1/8 teaspoon pepper. Place on hot grill grates for 3-5 minutes. Flip and continue to cook the other side 3-5 minutes. During the last 2 minutes of cooking, place the bun halves on the coolest part of the grill and watch closely to prevent burning. Grill buns for 2 minutes or until toasted and lightly browned.
To assemble the sandwiches spread an equal amount of pimento cheese on each toasted bun bottom. Top each with a slice of grilled green tomato and 2 slices of sweet and spicy bacon per sandwich. Serve immediately.