Put the julienned carrots, daikon, and cucumber in a medium bowl and season with ½ teaspoon salt and the brown sugar. Add the fish sauce and chile, toss well and let marinate for 5 minutes.
Add the bean sprouts, scallions, basil, mint, and a squeeze or two of lime juice to the julienned vegetables. Split the baguette lengthwise and line the bottom half with the lettuce leaves and cilantro sprigs. Spoon the vegetables into the loaf.
Distribute the avocado and eggs evenly, salt lightly add the top half of the baguette, and press down gently. Cut into 4 sandwiches.