1. Combine 1/4 cup soy sauce, honey, vinegar, 1 tablespoon oil, hoisin, 1 tablespoon chile paste, and 3 garlic cloves, stirring well with a whisk; place mixture in a heavy-duty zip-top plastic bag. Place pork in bag; seal. Marinate in refrigerator 8 hours or overnight, turning occasionally.
2. Preheat oven to 450°.
3. Remove pork from bag; reserve marinade. Place a roasting rack in a small roasting pan; fill pan with water to a depth of 1/2 inch. Place pork on rack. Roast pork at 450° for 15 minutes. Baste pork with some of reserved marinade. Turn pork over; baste. Reduce oven temperature to 400°. Cook pork an additional 40 minutes, basting every 10 minutes. Discard remaining marinade. Let pork stand 10 minutes; thinly slice.
4. Prepare noodles according to package directions; drain. Combine remaining 1/4 cup soy sauce, remaining 2 tablespoons oil, remaining 1 tablespoon chile paste, remaining 2 garlic cloves, juice, and sugar in a large bowl, stirring well. Add noodles to bowl; toss to coat. Divide noodles evenly among each of 6 bowls. Combine cilantro and mint; sprinkle about 1 tablespoon herb mixture over each serving. Divide pork evenly among bowls.