Bring a large pot of salted water to a boil.

Add soba noodles to boiling water.

Cook soba noodles until al dente, about 5 minutes.

Drain the soba noodles.

Transfer the drained noodles to a medium bowl to keep warm.

In a small bowl, combine soy sauce, lemon juice, and 1 tablespoon of minced fresh ginger to make a soy-ginger mixture.

Brush salmon fillets with a little soy-ginger mixture on both sides.

Dredge the brushed salmon fillets in sesame seeds, coating them evenly.

Heat vegetable oil in a large nonstick skillet over moderately high heat.

Add the sesame-crusted salmon fillets to the hot pan.

Cook salmon until the sesame seeds are golden and the fish is just cooked through, about 5 minutes per side.

In the bowl with soba noodles, add sesame oil, coarsely chopped green onions, remaining 1 tablespoon of ginger, and remaining soy-ginger mixture.

Toss the soba noodles with the added ingredients to combine well.

Transfer the soba noodles to serving bowls.

Top the soba noodles with the cooked salmon fillets.

Serve immediately.