Make pork: Mix soy sauce, oil, vinegar and honey in a large ziplock bag. Add pork. Seal bag. Refrigerate, turning bag occasionally, for 4 hours or up to overnight.
Preheat oven to 375°F. Remove pork from marinade. Pat dry. Place on a rack in a roasting pan. Pour marinade into a pan; bring to a boil. Reduce heat. Simmer 5 minutes. Remove from heat. Pour 1 cup water into bottom of roasting pan. Roast for 15 minutes. Baste pork with marinade. Roast until a meat thermometer inserted in thickest part reads 145°F, 10 to 15 minutes longer. Let pork rest for 10 minutes.
Make noodles: Bring a pot of water to a boil. Cook noodles until tender, about 3 minutes or as package label directs. Drain; rinse noodles in cold water, then drain again. In a bowl, whisk peanut butter, vinegar, soy sauce, ginger, honey and sesame oil until smooth. In another bowl, toss noodles, carrots, scallions and bean sprouts with 1/2 cup of dressing (add more to taste, if desired). Divide among four lunch containers; top with sliced pork. Serve or cover and chill until ready to pack lunch.