Heat a griddle over medium heat. Butter the inside slices of each burger bun, then toast in the skillet until golden brown, 2 to 3 minutes. Set aside.
Heat a large skillet over low heat; pan-fry the bacon for 2 minutes, then increase heat to medium-high and continue to pan-fry until crispy, 5 to 7 minutes, turning often. Drain on paper towels and discard most of the bacon grease.
Cut each banana lengthwise into long slices, about 4 inches in length. Pour the sugar into a small bowl, then add in the banana slices to coat both sides in sugar. Fry the banana slices in the same skillet over medium heat until caramelized, 2 to 3 minutes.
Cook the burgers on a griddle over medium-high heat for 3 to 4 minutes per side, seasoning with salt and pepper. Press down firmly with a spatula to flatten the patties as they cook. A thermometer inserted into the center should read at least 160 degrees F (71 degrees C).
To assemble the burgers, lay down the bottom half the burger bun and spread on 1 tablespoon peanut butter. Place a burger patty on top, then add another tablespoon of peanut butter. Top with 2 to 3 slices of caramelized bananas, then 2 to 3 pieces of bacon. Drizzle with 1 teaspoon honey, then place the remaining burger bun on top.