Preheat oven to 400 degrees F. Line a baking sheet with parchment paper. Set aside.
In the bowl of a food processor, place the basil, garlic, pine nuts, lemon juice and zest. Pulse until finely chopped. With motor running, slowly drizzle the olive oil through the feed hole until the pesto is the desired thickness. Stop motor, remove lid and scrape down sides. Taste and add a pinch of salt, if needed. Set aside.
Toss the cubed new potatoes with a little olive oil and season well with sea salt and ground black pepper.
Arrange the salmon and potatoes on the lined baking sheet. Top the each salmon fillet with about 1 Tablespoon of the pesto. (Reserve remaining pesto for another use.) Place in oven and bake for 20-25 minutes, or until salmon is cooked thoroughly.
To serve, divide the arugula between two plates. Top with the salmon fillet and roasted potatoes. Squeeze with a little more fresh lemon juice. Serve.