For the honey mustard sauce: Mix together the mustard, honey and mayonnaise in a small bowl and refrigerate until ready to use.
For the fried chicken BLT melt: Preheat the oven to 400 degrees F. Line a baking sheet with foil.
Remove the poached chicken from the refrigerator and let come to room temperature.
Lay the bacon slices on the prepared baking sheet and bake until crisp, about 20 minutes. Drain on a paper-towel-lined plate.
Add 1 1/2 inches of oil to a high-sided cast-iron skillet (making sure you are below halfway) and heat until a deep-fry thermometer inserted in the oil registers 375 degrees F. While waiting for the oil to heat, toast the buns in the still-warm oven.
Whisk together the flour, salt, garlic powder, paprika and black pepper in a baking dish. In a separate baking dish, whisk together the buttermilk and hot sauce. Slice each chicken breast in half horizontally. Dredge the chicken through the buttermilk, letting any excess drip off, then through the flour. Carefully place in the hot oil and fry until golden and crisp, 1 to 2 minutes on each side. Remove to a paper-towel-lined plate to drain. Cover the chicken pieces immediately with the cheese slices so they can begin to melt.
Spread the cut sides of the buns with the honey mustard sauce. Add 2 pieces of fried chicken to each bottom bun, and top with 2 pieces of bacon, a piece of lettuce, a slice of tomato and more sauce if desired. Sandwich the buns together and enjoy.