Heat oven to 400ºF. Have 4 (18-inch) squares heavy-duty aluminum foil standing by.
Break up ramen noodles and divide evenly in center of each of the 4 pieces of aluminum foil. Stack the following ingredients on top of noodles, in this order: edamame, carrots, shrimp, scallions, red pepper flakes, and salt. Pull sides and corners of pouch up to form a small basket shape, leaving an opening at the top to pour in liquid.
In a small bowl, combine the vegetable broth, mirin, soy sauce, and sesame oil. Distribute about 1/2 cup liquid among the packets. Press foil together to seal. Place packets on a half-sheet pan and bake for 15 to 20 minutes. Check one packet for doneness: The shrimp should be opaque and most of the liquid should be absorbed. Rest 3 minutes before serving.