To make the pickled daikon and carrots, combine the carrot and daikon radish in a mason jar. In a small pot, whisk together the sugar, vinegar and 1/3 cup water. Bring to a simmer until sugar dissolves; let cool for 10 minutes. Pour the sugar mixture into the mason jar. Cover and place in the refrigerator for at least one hour.
To make the marinade, whisk together the hoisin sauce, soy sauce, honey, vinegar, sesame oil and pepper, to taste. Add the pork belly and gently toss to combine. Cover and place in the refrigerator for at least 30 minutes.
Heat 2 tablespoons olive oil in a cast-iron skillet. Add the pork belly and cook until crisp and browned, about 4-5 minutes; set aside.
To make the green onion mayonnaise, combine the mayonnaise, green onions and garlic in a small bowl.
Serve pork belly on rolls with pickled daikon and carrots, cucumber and green onion mayonnaise.