Bring a pot of salted water to a boil and cook the soba noodles until al dente, about 8 minutes. Drain and rinse under cold water; set aside.
Layer the basil evenly over the bottom of a steamer basket. In a small bowl, mix together the ginger, white and light green scallion slices and orange zest and scatter over the basil. Add the shrimp and top with the bell pepper and mushrooms.
Bring the vegetable broth to a simmer in the steamer base. Place the steamer basket on top and cover. Steam over medium heat until the shrimp are just cooked through, about 6 minutes. Remove the steamer basket and set aside, covered, to keep warm.
Season the vegetable broth to taste with salt and pepper. Add the cooled soba noodles to the simmering broth until heated through, about 1 minute. Divide the noodles and broth among 4 bowls and top with the shrimp, red bell pepper, mushrooms and dark green scallion slices.