Cook the soba noodles according to the package directions; rinse under cold water. In a small bowl, whisk together the soy sauce, lime juice, sugar, and ¼ cup water; set aside.
Meanwhile, heat the oil in a large saucepan over medium heat until the temperature registers 360° F on a deep-fry thermometer.
In a large bowl, whisk together the flour, seltzer, and baking soda. In batches, dip the shrimp and broccoli in the batter and fry in the oil until golden, 4 to 5 minutes.
Serve the shrimp and broccoli on the noodles with the soy-lime dipping sauce. Top with the scallions.