Thinly slice 1 chile; set aside. Stem and finely chop remaining 3 chiles (you should have about 5 tablespoons).
Stir together pork, ¼ cup hoisin, 2 teaspoons chili-garlic sauce, 2 teaspoons salt, 1 teaspoon pepper, and 3 tablespoons finely chopped chiles in a large bowl until combined. Roll into 24 balls (slightly larger than a golf ball). Place on a large rimmed baking sheet, loosely cover, and refrigerate.
Whisk lime juice and remaining ¼ cup hoisin, 1 teaspoon chili-garlic sauce, ¼ teaspoon salt, ¼ teaspoon pepper, and 2 tablespoons finely chopped chiles in a medium bowl. Gradually whisk in 6 tablespoons oil.
Cook noodles according to package directions. Rinse under cold water for 5 to 10 seconds. Drain well; transfer to large bowl. Toss with ½ cup dressing and remaining 1 tablespoon oil.
Preheat broiler with oven rack 8 inches from heat. Broil meatballs until browned and a thermometer inserted in meatballs reads 160°F, 10 to 15 minutes.
Gently toss noodles with carrots, lettuce, cucumber, and thinly sliced chile. Top with meatballs. Drizzle with remaining dressing and top with cilantro and peanuts.
