Peel and devein the shrimp, reserving the shells. Combine the shrimp shells with 6 cups of water in a stockpot. Bring to a boil and simmer until the broth tastes of shrimp, about 15 minutes. Strain and discard the shells.
Peel and remove the seeds from the tomato and cut into a fine dice. Soak the rice noodles in a small bowl of warm water until soft. Drain and reserve. Cut into manageable lengths, if desired.
Heat the oil in a deep saucepan and saute the garlic until just brown. Remove and discard. Add the shallots and cook over medium heat until soft. Add the balichao and cook until aromatic. Add the shrimp broth, bring to a simmer and add the shrimp, the rice noodles and the tomatoes. Cook gently until the shrimp just turns pink. Season with salt and pepper. Sprinkle with the scallions, stir to just wilt and serve.