For the jalapeno pimiento cheese: Drain 1 jar of the pimientos and place in a blender or food processor. Puree until smooth. Drain the second jar. Using an electric mixer, combine the Cheddar, cream cheese, pureed pimentos and diced pimientos, beating until smooth. Add the mayonnaise and jalapenos and mix until fully combined.
For the fried green tomatoes: Cut the ends off of the tomatoes and slice into 1/4-inch-thick slices. Season with 1 teaspoon salt and freshly ground pepper.
In a shallow bowl, whisk together the flour, cayenne pepper, paprika, 1/4 teaspoon salt, and a pinch of freshly ground pepper. In a second shallow bowl, whisk together the eggs and buttermilk. In a third shallow bowl whisk together the panko, cornmeal and remaining 1/2 teaspoon salt.
Working with one tomato slice at a time, first coat the tomato with the flour mixture, shaking off the excess. Then coat with the egg mixture, followed by the panko mixture. Transfer to a parchment-lined baking sheet. Repeat with the remaining tomatoes.
Heat 2 cups oil in a large skillet over medium heat until a pinch of panko sizzles when dropped in. Carefully place some of the tomatoes into the heated oil in a single layer. Fry until golden, 2 to 4 minutes per side. Drain on a paper towel-lined baking sheet. Repeat the frying process with the remaining tomatoes, changing the oil if the particles left in the oil between batches begin to burn.
For the BPT: Cook the bacon in a large saute pan over medium-high heat until desired crispness, 8 to 10 minutes. Gently spread one side of each slice of bread with the jalapeno pimiento cheese. Arrange the bacon, then the fried green tomatoes and then the lettuce on 4 slices. Top with the remaining slices, and cut each sandwich in half. Serve immediately.