Preheat the oven to 400 degrees F.
Combine the chicken broth, mirin, soy sauce, lime juice, sesame oil, fish sauce and chili paste in a large bowl.
Make the pouches: Place 2 large sheets of foil side by side on a work surface. Top each with an 11-by-15-inch piece of parchment. Divide the noodles between the 2 pieces of parchment.
Top with the shrimp, mushrooms, shallots and green onions. Lift the sides of each piece of foil to create a bowl-like shape. Pour some of the chicken broth mixture over the noodles.
Bring the top of the parchment together and fold the edges to form a seal, making sure not to leak any liquid. (The foil should remain open like a bowl.) Transfer the bowls to a rimmed baking sheet and bake until the shrimp is cooked and the noodles are tender, 15 to 20 minutes.
To serve, transfer the parchment pouches to serving plates and open, or pour the contents of the pouches into bowls. Garnish with the cilantro.