In a small bowl, whisk together the soy sauce, toasted sesame oil, rice vinegar, honey, grated ginger, and minced garlic to create the dressing.
Bring a large pot of water to a boil. Cook the soba noodles for 4-5 minutes until al dente, then drain and rinse immediately under cold running water to stop the cooking process.
Pat the salmon fillets dry with paper towels and season lightly with salt and black pepper.
Heat olive oil in a non-stick skillet over medium-high heat. Place salmon skin-side down and sear for 4 minutes. Flip and cook for an additional 3-4 minutes until the internal temperature reaches 145°F (63°C).
In a large mixing bowl, toss the cold soba noodles with half of the prepared dressing until evenly coated.
Divide the dressed noodles between two bowls.
Top each bowl with a salmon fillet, edamame, and sliced cucumber.
Drizzle the remaining dressing over the toppings and garnish with toasted sesame seeds and sliced green onions.