Heat canola oil in a large saucepan set over medium-high heat. Add ginger and saute for 2 minutes. Add garlic and cook, stirring constantly, for 30 seconds. Add chicken broth and bring it to a boil. Add soba noodles and cook until tender, about 5 minutes. Stir in soy sauce and turn down the heat until the broth is simmering.
Add the shrimp to the broth and simmer until just cooked through. Avoid overcooking the shrimp or it will become rubbery.
While the soba noodles are cooking, heat canola in a large skillet set over medium-hight heat. Add mushroom and cook until almost tender, 4 to 5 minutes. Stir in broccoli florets and cook until broccoli is tender-crisp and the mushrooms are starting to brown.
Divide the mushroom and broccoli mixture between four bowls.
Ladle the broth, noodles and shrimp into the bowls. Serve.