Bring a large pot of water to a boil. Preheat broiler with rack 4 in. from heating element.
Meanwhile, put steak in a medium bowl and pour in 2 tbsp. soy sauce, turning steak to coat. Let sit for a few minutes. Make dressing: In a small bowl, combine lime juice, fish sauce, sugar, chile, and remaining 1 tbsp. soy sauce; set aside.
Cook noodles in boiling water until tender, about 2 minutes, then drain.
Broil steak on a broiler pan, turning once, until done the way you like, about 12 minutes for medium-rare. Let rest 10 minutes, then slice thinly.
Meanwhile, in a small saucepan, heat oil until it registers 350° on a candy thermometer. Dust shallots evenly in flour to coat and cook in oil, carefully stirring, until browned, about 4 minutes. Transfer to paper towel to drain.
In a large bowl, combine noodles, sliced steak, herbs, and half the reserved dressing. Divide mixture among 4 plates, sprinkle evenly with shallots, and serve remaining dressing on the side.
Note: Nutritional analysis is per serving.