Pickle the Carrots and Daikon: Combine carrots, daikon, salt, and sugar in a small bowl and toss to coat. Allow to rest for 10 minutes until the liquid has been drawn out of the vegetables and the salt and sugar are completely dissolved. Add vinegar and water and transfer to a small, sealable container. Let it sit at room temperature for 1 hour.
Cook the bacon: Cook bacon in a nonstick skillet over medium-low heat until crisp and rendered, flipping once halfway through cooking. Transfer to a paper towel-lined plate (leave bacon grease in the skillet).
Cook the eggs: Increase heat to medium-high. Add eggs, immediately reduce heat to medium, and cook, spooning hot bacon fat over egg tops as they cook until set to desired consistency. Transfer eggs to the paper towel-lined plate with bacon.
Toast the bread and assemble: Split the bread in half lengthwise, leaving a hinge. Toast bread in the oven or toaster oven until golden brown, about 3 minutes. Spread both sides with mayonnaise. Layer bacon strips along the bottom and top with eggs. Top with pickled carrots, daikon, cucumber slices, and cilantro. Season with salt and black pepper.
Prepare the fruit: Wash and prepare the fruit as directed above.
Serve: Serve the breakfast banh mi immediately with sliced apples, bananas, and orange juice.