Prepare the ingredients per the instructions above.
Combine carrots, daikon, salt, and sugar in a small bowl and toss to coat. Stir until the salt and sugar are completely dissolved. Add vinegar and water and transfer to a small, sealable container. Let sit at room temperature until needed. Drain well before using.
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).
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 the whites are firm. Then set aside.
Split the roll 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 pepper.
Serve immediately with fruit and orange juice.