In a small bowl, whisk 2 tablespoons of the olive oil with the lemon juice and mustard and season with salt and pepper.
In a large nonstick skillet, heat 1 tablespoon of the olive oil. Season the salmon with salt and pepper. Cook the salmon skin side down over moderately high heat until the skin is very crisp and golden, about 5 minutes. Flip the fillets and cook until opaque in the center, about 4 minutes. Transfer the salmon to plates, skin side up. Pour off the oil in the skillet.
Heat the remaining 1 tablespoon of olive oil in the pan. Add the tomatoes and shallot and cook over moderately high heat, stirring occasionally, until browned in spots, about 2 minutes. Season with salt and pepper.
In a large bowl, toss the arugula with the basil, dressing, tomatoes and shallots. Mound the salad beside the salmon and serve.