Preheat the oven to 400°F. Heat 1 tablespoon of vegetable oil in a large skillet over medium-high heat. Brush the tops of the salmon fillets with the sesame oil and season with salt and pepper. Add to the pan and cook for 2 to 3 minutes, until the skin is crispy and golden brown. Flip the fish over and transfer to the oven. Cook for 8 to 10 minutes, until the fish flakes easily and is cooked through.
Meanwhile, heat the remaining ¼ cup of vegetable oil in a small, shallow pan over medium heat, until it registers 350°F. Add the capers and fry for 30 seconds, then drain on paper towels.
Whisk together the lime juice, ginger, honey, olive oil, and a pinch of salt in a small bowl to combine.
Toss together the baby greens, tomatoes, and fried capers in a large bowl. Drizzle the vinaigrette over the salad and toss to combine. Divide the salad between four plates and top each with a salmon filet.