Peel and mince the ginger; transfer to a medium bowl.
Add half of the lime juice (save the rest for the salad), soy sauce, and olive oil to the ginger; whisk together.
2 tbsp soy sauce
2 tbsp extra virgin olive oil
Place the salmon, skin-side-up, in the sauce. Set the bowl aside.
1 ½ lb salmon fillets
Preheat a skillet over medium heat.
Once the skillet is warm, measure out the sesame seeds and add to the skillet. Cook, stirring frequently, until they are golden brown, 2 to 3 minutes. Once done, transfer to a small bowl.
2 tbsp sesame seeds
Add olive oil to the skillet and swirl to coat the bottom.
2 tbsp extra virgin olive oil
Place the salmon, skin-side down, in the skillet; cook for 3 to 4 minutes on one side, then flip and pour in the remaining sauce. Continue to cook until the flesh is opaque, another 2 to 3 minutes.
Combine the remaining lime juice, olive oil, sesame oil, soy sauce, and honey in a large bowl; whisk together.
2 tbsp extra virgin olive oil
2 tbsp toasted sesame oil
2 tbsp soy sauce
2 tsp honey
Quarter the cabbage lengthwise, then cut out and discard the core; thinly slice crosswise and add to the large bowl.
Trim the ends and peel the carrots; discard the trimmings and coarsely grate the carrots. Add to the cabbage.
Toss the salad until well combined.
To serve, arrange the salad on a plate and place the salmon on top. Enjoy!